WORKBOOK SAMPLER
Chapter 7: Polygons
Nelson Mathematics for Apprenticeship and Workplace 12
Nelson Mathematics for Apprenticeship and Workplace resources are comprehensive supplementary workbooks that are carefully designed to engage students in real-life contexts of mathematics.
Three components are available for Nelson Mathematics for Apprenticeship and Workplace 12:
Student Workbook• 300+ page workbook• Each lesson includes prompts, examples, and exercises scaffolded in
manageable steps• Predictable layout assists students with weak organizational skills• Written at an appropriate reading level for struggling students• Real-world connections embedded throughout• Supports 100% of the outcomes in the new curriculum
Solutions Book (Available in print format or non-printable CD-ROM)• Student Workbook with answers provided on every page for teacher reference
Computerized Assessment Bank• ExamView® software makes creating customized practice sheets and tests a
breeze, with hundreds of multiple choice, true/false, and short answer questions to choose from
For more information, visit www.nelson.com/wncpmath/apprenticeship
1
Nelson Mathematics for Apprenticeship and Workplace 12
Table of Contents Chapter 1 Buying or Leasing a Vehicle Getting Started 1.1 Buying a New Vehicle 1.2 Buying a Used Vehicle 1.3 Operating Costs for a Vehicle 1.4 Who’s Buying What? Mid-Chapter Review 1.5 Leasing a Vehicle 1.6 Lease or Buy? 1.7 Vehicle Options and Technology Chapter ReviewChapter Test
Chapter 2 Measuring Instruments Getting Started2.1 Precision 2.2 Precision and Calculations 2.3 Solving a Measuring Puzzle Mid-Chapter Review 2.4 Precision and Accuracy 2.5 Uncertainty in Measurements Chapter Review Chapter Test
Chapter 3 Statistics Getting Started 3.1 Mean 3.2 Weighted Mean 3.3 Median 3.4 Mode 3.5 Which Score is Higher? Mid-Chapter Review 3.6 Interpreting Data 3.7 Percentiles Chapter Review Chapter Test
This Sampler contains Chapter 7
NEL Chapter 7 Polygons
2
Nelson Mathematics for Apprenticeship and Workplace 12
Chapter 4 Linear Relations Getting Started 4.1 Describing Relations 4.2 Interpreting Linear Relations 4.3 Direct and Partial Relations Mid-Chapter Review4.4 Equations of Linear Relations 4.5 Creating a Number Trick 4.6 Scatter Plots 4.7 Scatter Plots and Technology Chapter Review Chapter Test
Chapter 5 Career Planning Getting Started 5.1 Exploring Career Options 5.2 Researching Your Career Choice 5.3 Planning for Training Costs 5.4 Writing a Resumé 5.5 Financing Your Lifestyle Chapter Project
Chapter 6 Operating a Small Business Getting Started 6.1 Business Opportunities 6.2 Business Expenses 6.3 Planning for Taxes 6.4 Sidewalk Sale Game Mid-Chapter Review6.5 Improving Profitability 6.6 Break-Even Point Chapter Review Chapter Test
Apprenticeship and Workplace 12 NEL
3
Nelson Mathematics for Apprenticeship and Workplace 12
Chapter 7 Polygons Getting Started 7.1 Triangles 7.2 Quadrilaterals 7.3 Creating Polygon Puzzles Mid-Chapter Review7.4 Regular Polygons 7.5 Applications of Polygons Chapter Review Chapter Test
Chapter 8 Transformations Getting Started 8.1 Translations 8.2 Reflections 8.3 Rotations Mid-Chapter Review8.4 Dilations 8.5 Dilations and Technology 8.6 Combining 2-D Transformations 8.7 Solving a Transformation Puzzle Chapter Review Chapter Test
Chapter 9 Trigonometry Getting Started 9.1 Exploring the Sine Law 9.2 Solving Sine-Law Problems 9.3 Reversing Triangle Puzzle Mid-Chapter Review9.4 Exploring the Cosine Law 9.5 Solving Cosine-Law Problems 9.6 Choosing the Sine Law or Cosine Law Chapter Review Chapter Test
NEL Chapter 7 Polygons
Apprenticeship and Workplace 12 NEL4
Nelson Mathematics for Apprenticeship and Workplace 12
Chapter 10 Probability Getting Started 10.1 Experimental Probability 10.2 Theoretical Probability 10.3 Three-Cup Guessing Game Mid-Chapter Review10.4 Interpreting Odds 10.5 Making Decisions Chapter Review Chapter Test
Chapter 11 Owning a Home Getting Started 11.1 Qualifying for a Mortgage 11.2 Closing Costs 11.3 Mortgage Payments Mid-Chapter Review 11.4 Managing Housing Costs 11.5 Mortgages and Technology 11.6 Solving Map Puzzles Chapter Review Chapter Test
Glossary
7777777Polygons
Zahra is a beekeeper near Melfort. The cells in a honeycomb are hexagons. This makes it possible for the bees to pack a lot of honey into a small space. It also gives the honeycomb strength.
A. How can you tell if a shape is a hexagon?
B. Draw a 2-D shape that is not a hexagon. How is your shape the same as the hexagon drawn on the honeycomb? How is it different?
e.g., It has six straight sides and six vertices.e.g., It has six straight sides and six vertices.
e.g., Same: Both have straight sides. e.g., Same: Both have straight sides.
Different: My shape has three straight sides and three Different: My shape has three straight sides and three
vertices. The sides and the angles of my shape are not equal. vertices. The sides and the angles of my shape are not equal.
The sides and the angles of the hexagon are equal.The sides and the angles of the hexagon are equal.
B. e.g.,
Chapter 7 Polygons 161NEL
5NEL Chapter 7 Polygons
7777777 GettingGettingGettingGettingGettingGettingGettingGetting
1. A triangle is a polygon with three straight sides and three vertices. Use side lengths to classify the triangles in the picture of a crane below.
a) Which triangle is an equilateral triangle?
b) Which triangle is an isosceles triangle?
c) Which triangle is a scalene triangle?
2. Use angles to classify the triangles in the picture of a crane.
a) Which triangle is an acutetriangle?
b) Which triangle is an obtusetriangle?
c) Which triangle is a righttriangle?
3. Measure the side lengths and interior angles of the triangles below. Use millimetres for the side lengths. Record the measurements on the diagrams.
You will need• a millimetre ruler• a protractor
equilateraltriangle
a triangle with three equal sides
isoscelesisoscelestriangle
a triangle with exactly two equal sides
scalene triangle
a triangle with no equal sides
acute triangle
a triangle with each angle less than 908
obtuseobtuse triangletriangle
a triangle with one angle that is greater than 908
rightright triangletriangle
a triangle with one angle that is equal to 908
C07-F02-AW12SB
CrowleArt Group
3rd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
1
2
3
4. Use the triangles in Question 3. What do you notice about the measure of the angle opposite the longest side in each triangle?
34 mm
34 mm
48 mm
4545°
4545°
1
35 mm 35 mm
35 mm
60°
60°
60°
2
60 mm
36 mm 36 mm
33°
114°
33°3
60 mm
36 mm
36 mm
33°
114°
33°
4
22 mm22 mm
65°
25°
55 mm
50 mm5
3
2
1
3
1
2
The largest angle is opposite the longest side.The largest angle is opposite the longest side.
162 Apprenticeship and Workplace 12 NEL
6 Apprenticeship and Workplace 12 NEL
5. Which triangles in Question 3 match each description?
a) equilateral triangle:
b) scalene triangle:
c) obtuse triangle:
d) regular polygon:
6. a) Which two triangles in Question 3 are congruent?
b) Two angles in triangle 5 are complementary. What are the measures of these angles?
7. Use the marks on each shape. Fill in the blanks below.
a) I J
H K
side HI 5 side
side 5 side
b) B C
D
/ /
c) Q
P S
R
QR and PS are .
8. a) The diagram below shows a transversal crossing two parallel lines. Record the angle measures on the diagram. Do not measure the angles.
160°
160°20°
20°160°
160°20°
20°
b) What are the measures of two opposite angles in the diagram?
c) What are the measures of two supplementary angles in the diagram?
9. Dawn plans to install a ridge vent on a roof. This will cool the attic. The angle of the vent needs to equal /RST at the peak of the roof. RST at the peak of the roof. RSTDawn knows the measurements in the diagram.
a) What type of triangle is nRST? RST? RST
b) What is the measure of /RST? How do you know?RST? How do you know?RST
complementaryangles
two angles whose sum is 908
regular polygon
a closed shape with all sides equal and all angles equalangles equal
transversal
a line that intersects two or more lines
supplementaryangles
two angles whose sum is 1808
opposite angles
non-adjacent angles that are formed by two intersecting lines
30 ft 30 ft
38°38°R T
S
C07-F12-AW12SB
CrowleArt Group
3rd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
2
5
3 and 4
2
3 and 4
658 and 258
IJ
KJ
HKDBC DCB5DBC DCB5 /DBC DCB/
parallelparallel
e.g., 20e.g., 208 and 208 OR 1608 and 1608
1608 and 208
e.g., isoscelese.g., isosceles
The measure of /RST is 104RST is 104RST 8. The sum of the angles
in any triangle is 1808. 1808 2 388 2 388 5 1048
Chapter 7 Polygons 163NEL
7NEL Chapter 7 Polygons
Triangles7777777.7.7.1111111You will need• string• scissors• plain paper• a millimetre ruler• a protractor
Try TheseMake a paper triangle. Draw a dot at each vertex. Cut the triangle so that Make a paper triangle. Draw a dot at each vertex. Cut the triangle so that each vertex is separate. Show that the sum of the angles is 180each vertex is separate. Show that the sum of the angles is 1808.
ReflecTinGSuppose that the sum of the lengths of the two shortest
sides is less than the length of the longest side. Can these three pieces of string make a triangle? Explain.
A C
B
M
Cut three pieces of string that you can use to make a triangle. How many different triangles can you make?
1 Place your string on paper to make a triangle. Mark the vertices with a pencil. Join the vertices.
2 What are the side lengths?
3 What are the angle measures?
4 Two triangles are different if they are not congruent. Are any different triangles possible with your side lengths?
5 Compare your triangle with other students’ triangles. Could anyone make more than one triangle?
Example 1The bamboo stems in this photograph create The bamboo stems in this photograph create an isosceles triangle. An isosceles triangle an isosceles triangle. An isosceles triangle has two equal sides called legs. The interior . The interior angles opposite the legs are also equal.
Do all isosceles triangles have these properties?
SolutionA. Find the midpoint of side AC.
Label it M. Draw MB.
B. What are the side lengths, in millimetres?
nABMnABMn :
nCBM:
property
a characteristic that is shared by all the members of a group
e.g., 128 mm, 175 mm, and 184 mme.g., 128 mm, 175 mm, and 184 mm
e.g., 66e.g., 668, 748, and 408
no
MPS
1st pass
Try These e.g.,
no
1. e.g., 1. e.g.,
19 mm, 50 mm, and 47 mm
19 mm, 50 mm, and 47 mm
164 Apprenticeship and Workplace 12 NEL
8 Apprenticeship and Workplace 12 NEL
C. Is nABMnABMn congruent to ABM congruent to ABM nCBM? How do you know?
D. Kate said that this property is a property of all isosceles triangles. Do you agree with Kate? Explain. Include a diagram.• The angles opposite the equal legs are equal.
Example 2Pavlo is a carpenter. He uses triangular brackets for shelving. The sides of each bracket extend past the vertices to create exterior angles. What types of triangles have this property?• Each exterior angle is 908 or greater.
SolutionA. Measure the interior and exterior angles in the acute triangle
below. Record the angle measures on the diagram.
Acute triangle: Obtuse triangle:
B. Draw an obtuse triangle in Part A. Extend one side at each vertex to create three exterior angles. Measure the interior and exterior angles. Record the measures. Are any exterior angles acute?
C. Is the following a property of all triangles? Explain.• Each exterior angle is 908 or greater.
D. What triangles have the property in Part C?
C07-F17-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
150°
120°
90°
ReflecTinGWhy is showing that something
is not a property easier than
showing that it is a property?
35° 110°
145°
70°
75°
105°
Use the triangular bracket above as an example of a right triangle.
Hint
Yes. e.g., They are congruent because only one triangle is Yes. e.g., They are congruent because only one triangle is
possible with these sides. OR They are the same size and possible with these sides. OR They are the same size and
shape.shape.
e.g., Yes, I agree. If you draw a centre line, you get two e.g., Yes, I agree. If you draw a centre line, you get two
congruent triangles. So the corresponding angles are equal.congruent triangles. So the corresponding angles are equal.
yesyes
D FM45° 45°
35 mm
20 mm 20 mm
E
D. e.g.,
e.g.,
No. e.g., One exterior angle on the obtuse triangle is less No. e.g., One exterior angle on the obtuse triangle is less
than 908.
acute triangles and right trianglesacute triangles and right triangles
28°
160°
152°
132°20°48°
Chapter 7 Polygons 165NEL
9NEL Chapter 7 Polygons
Practice 1. Use your triangles from Example 2.
a) The sum of the interior angle plus the exterior angle is the same at each vertex. What is this sum?
b) Why does it make sense that each vertex has the same sum?
When you extend one side, you create angles that form . Angles that form have a sum of .
c) Is this a property for all triangles? Explain.• The sum of the interior angle plus the exterior angle
is 1808.
2. Cables on the Esplanade Riel Bridge in Winnipeg illustrate many types of triangles.
Circle the types of triangles that have each property.
a) Some sides are equal.
equilateral triangle isosceles triangle scalene triangle
b) Some exterior angles are equal.
equilateral triangle isosceles triangle scalene triangle
c) No interior angles are equal.
equilateral triangle isosceles triangle scalene triangle
d) All three exterior angles are 908 or greater.
acute triangle obtuse triangle right triangle
e) Each exterior angle is equal to the sum of the interior angles at the other two vertices.
acute triangle obtuse triangle right triangle
3. a) What is one property of isosceles triangles that is not a property of all triangles?
b) What is one property of isosceles triangles that is a property of all triangles?
ReflecTinGDoes it matter which side of a triangle you
extend to make an exterior angle?
Explain.
Use the diagrams and definitions of different types of triangles in Getting Started.
Hint
1808
twoa straight linea straight line a straight linea straight line
1808
Yes. e.g., You always create an exterior angle by extending
a side. The interior angle and exterior angle will always
form a straight line.
e.g., Isosceles triangles have exactly two equal sides.
e.g., The sum of the interior angles is 1808.166 Apprenticeship and Workplace 12 NEL
10 Apprenticeship and Workplace 12 NEL
4. Use the angle measures to calculate the unknown angles in each triangle. Include interior angles and exterior angles. Record the measurements on the diagrams.
137°
75°
148°
43°105°
1
32°
60°
30°
30°
150°
150°
2
120°
125°
145°
160°
35°3
55°
20°
5. Use the triangles in Question 4. Complete this chart.
TriangleSum of 3 interior
anglesSum of 3 exterior
angles
Sum of 3 interiorangles 1 sum of3 exterior angles
1
2
3
6. Marcel’s crew builds A-frame cabins in Tofino.• The balcony is parallel to the base of a cabin. • The front of this cabin is an equilateral triangle. • The section above the balcony is also an
equilateral triangle.
Marcel wonders about this question.• Does drawing a line parallel to the base of any
triangle create a second triangle with angles that are equal to those in the original triangle?
a) Test Marcel’s idea. • Draw a triangle. Draw a line through your triangle so
that the line is parallel to the base.
Are the angles in the small triangle equal to the angles in the large triangle?
b) Compare your results with a classmate’s results. Did your classmate get the same results?
c) Will adding a line that is parallel to the base always create a smaller triangle with the same angles? Explain.
C07-F24-AW12SB
CrowleArt Group
3rd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
60°
60° 60°
60°60°
ReflecTinGDo you think that
the sum of the interior angles and the exterior angles is the same for all triangles? Explain.
One way to draw parallel lines is to draw along both sides of a ruler.
Hint
180818081808
360836083608
540854085408
yesyes
yesyes
Yes. e.g., One angle is shared by both triangles. The other two angles are corresponding
angles, formed by transversals that meet the parallel lines at the same angle. So each
angle in the small triangle has a matching equal angle in the large triangle.
65°
25°
25°
6. a) e.g.,
Chapter 7 Polygons 167NEL
11NEL Chapter 7 Polygons
Brady installs stained-glass windows in Victoria. How can you describe the quadrilaterals in this window?
C07-F26-AW12SB
CrowleArt Group
3rd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
square
rectangletrapezoid
rhombus
parallelogramkite
triangle (not aquadrilateral)
1 Label an example of each convex quadrilateral in Brady’s window. Draw an arrow to the quadrilateral.
Convex quadrilaterals
A rectangle has four 908 angles.
A square is a rectangle with four equal sides.
A parallelogram has opposite sides that are parallel and equal.
A rhombus is a parallelogram with four equal sides.
A trapezoid has only one pair of parallel sides.
A kite has two pairs of equal sides that are not opposite sides. If all four sides are equal, the quadrilateral is a rhombus.
2 Some polygons have more than one name. What are three other names for a square?
3 Label a polygon in the window that is not a quadrilateral. How do you know that it is not a quadrilateral?
Quadrilaterals7.27.27.27.27.27.27.27.27.27.27.27.27.27.27.27.27.27.2You will need• coloured pencils• a millimetre ruler • a protractor
Try These
Circle the polygons.Circle the polygons.
quadrilateral
a polygon with four straight sides and four vertices
convex
a polygon with no interior angles that are greater than 1808
e.g., A quadrilateral has four sides and four vertices. e.g., A quadrilateral has four sides and four vertices.
This triangle has three sides and three vertices.iangle has three sides and three vertices.
rectangle, parallelogram, and rhombusrectangle, parallelogram, and rhombus
e.g.,
168 Apprenticeship and Workplace 12 NEL
12 Apprenticeship and Workplace 12 NEL
Example 1Elena is a pastry chef in Fort Qu’Appelle. She cut these square pastries along a diagonal. This makes two congruent triangles. What other quadrilaterals have this property?
SolutionA. Draw diagonals to form triangles. Use a different colour for
each diagonal in each quadrilateral.
squarerectangle parallelogram kite trapezoid
irregularquadrilateral
rhombus
concavequadrilateral 1
concavequadrilateral 2
B. Name quadrilaterals with each property.
Property Quadrilaterals
Both diagonals make congruent triangles.
One diagonal makes congruent triangles.
No diagonals make congruent triangles.
Example 2Tessa is a carpenter in Whitehorse. She needs to check that a window frame is a rectangle. She only has a tape measure. How can she use the properties of a rectangle to check?
SolutionA. Measure the side lengths and diagonals in each quadrilateral.
Record them on the diagrams.
B. How can Tessa use the properties of a rectangle?
If the window frame is a rectangle, the opposite sides are and the diagonals are .
30 mm
30 mm
20 mm20 mm 36 mm36 mm36 mm
30 mm
30 mm
20 mm
30 mm
41 mm
20 mm
ReflecTinGHow do you know
if each result is a property of all quadrilaterals
that are the same type? Use side
lengths to explain.
diagonal
a line segment joining opposite vertices
C07-F28-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
irregular
a quadrilateral with different side lengths and different angle different angle measures
concave
a polygon with an interior angle that is greater than 1808
rectangle, parallelogram, rhombus, and square
kite and concave quadrilateral 1
trapezoid, irregular quadrilateral, and concave quadrilateral 2
equalequal equalequal
Chapter 7 Polygons 169NEL
13NEL Chapter 7 Polygons
Practice 1. Which convex quadrilaterals have each property?
a) two pairs of equal sides:
b) four right angles:
c) equal diagonals:
d) equal angles at opposite vertices:
2. How can you use properties to show that a rectangle is a parallelogram? A rectangle is a parallelogram because it has
.
3. The diagonals in a square are perpendicular. The diagonals cross at their midpoints. Record the names of other types of quadrilaterals to complete the chart.
PropertyA quadrilateral with
this propertyA quadrilateral without
this property
Diagonals are perpendicular.
Diagonals cross at their midpoints.
4. a) Show that the exterior angles of all quadrilaterals have the same sum.• At each vertex, the measure of the
interior angle plus the measure of the exterior angle equals .
• There are vertices. The total sum of all the interior and exterior angles of a quadrilateral is (( )) 5 .
• The sum of the interior angles is .• The sum of the exterior angles is 2 5 .• The sum of the exterior angles of any quadrilateral
is .
b) Do all quadrilaterals have diagonals that are perpendicular? Explain.
Draw some quadrilaterals. Measure the exterior angles to test your answer for Question 4.
Hint
Use diagrams from Example 1 to help you with Question 3.
Hint
rectangle, square, parallelogram, rectangle, square, parallelogram,
and rhombus
rectangle and squarerectangle and square
rectangle and squarerectangle and square
rectangle, square, rectangle, square,
parallelogram, and rhombusparallelogram, and rhombus
e.g., kite e.g., parallelogram
e.g., rhombus e.g., kitee.g., rhombus e.g., kite
1808
four1808 72084
3608
7208 3608 3608
3608
opposite sides that are parallel and equalopposite sides that are parallel and equal
No. e.g., The parallelogram, trapezoid, and irregular quadrilateral
in Example 1 do not have diagonals that are perpendicular.
170 Apprenticeship and Workplace 12 NEL
14 Apprenticeship and Workplace 12 NEL
5. Jay makes picture frames. The interior angles of the square picture frame have a sum of 3608. How can you draw a diagonal to show that all quadrilaterals have this property?
6. An isosceles trapezoid is cut from an isosceles triangle. It has two equal sides and two parallel sides. The parallel sides are called bases.
a) Use the isosceles triangle at the right. Draw a line parallel to the base to make an isosceles triangle. Measure to check that there are two equal side lengths in the trapezoid.
b) What are two properties of your isosceles trapezoid?
c) Compare your isosceles trapezoid with isosceles trapezoids drawn by your classmates. What is one property that is shared by all the isosceles trapezoids?
7. When you join the midpoints of all four sides of a quadrilateral, you always get the same type of polygon. Test some quadrilaterals. What is the polygon?
8. Darcy is cutting glass for a window that is a rhombus. She knows that the sides are 10 in. long.
Does she have all the information she needs to cut the glass? Explain. Include a diagram.
Think about • side lengths• angle measures• diagonals
Hint
C07-F40-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
4(90°) � 360°
10 in.10 in.
e.g., I looked at one diagonal in each quadrilateral
in Example 1. You get two triangles. The sum of the
interior angles of each triangle is 1808. The sum of the
interior angles of both triangles is 2(1808) 5 3608.
e.g., one pair of equal sides and two pairs of equal
angles OR equal diagonals
e.g., one pair of equal sides OR two pairs of congruent
angles OR two different angles that add to 1808 OR two
isosceles triangles and two congruent triangles that are
formed where the diagonals meet
No. e.g., She also needs to know the angle measures. There are
many rhombuses such as a square with the same side lengths.
7. e.g.,
parallelogramparallelogram
8. e.g.,
Chapter 7 Polygons 173NEL
15NEL Chapter 7 Polygons
The convex polygons below are made of squares and triangles.
pentagon hexagon
A. Use 12 toothpicks to make a different convex hexagon with squares and triangles. Draw your hexagon.
B. Use 12 toothpicks to make four other convex shapes. Make each shape out of smaller polygons. Draw your shapes.
C. Create a puzzle about a convex polygon made of smaller polygons. • Tell how many toothpicks to use. • Name the shape. • Draw the solution.
Trade puzzles with a partner. Solve each other’s puzzles.
creating Polygon Puzzles7.37.37.37.37.37.37.37.37.37.37.37.37.3You will need• 12 toothpicks
Here are names of polygons:
5 sides: pentagon6 sides: hexagon7 sides: heptagon8 sides: octagon9 sides: nonagon
10 sides: decagon12 sides:
dodecagon
Hint
e.g.,
e.g., Use 14 toothpicks to make a pentagon. Draw your
pentagon.
CrowleArt Group
CrowleArt Group
CrowleArt Group
CrowleArt Group
CrowleArt Group
square pentagon pentagon parallelogram
e.g.,
C. e.g.,
172 Apprenticeship and Workplace 12 NEL
16 Apprenticeship and Workplace 12 NEL
1. Ty says that if you know all the angle measures in a triangle, you will know whether the sides are equal. Do you agree? Explain. Use diagrams.
2. Is each property true or false? Use diagrams to explain your answers.
a) The midpoints of the three sides of an equilateral triangle are joined to form four small triangles. The area of each small triangle is 14 of the area of the original equilateral triangle.
b) The diagonals of a convex quadrilateral always create two pairs of equal angles where they intersect.
3. Hayley is the lighting director for a theatre in Manitoba. She wants to place a spotlight so that it shines on the centre of a rectangular stage.
How can Hayley use a property of rectangles to find the centre of the stage? Use the rectangle at the right in your explanation.
Mid-chapter
AW12 0176519637
Figure Number C07-F59-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F59 -AW12.ai
Yes. e.g., If three angles are equal, then the triangle is an
equilateral triangle with three equal sides. If two angles are
equal, the triangle is an isosceles triangle with two equal sides.
True. e.g., I tested some equilateral triangles. When
I joined the midpoints, I made four small congruent
triangles. So each triangle has 14 of the area of the
original equilateral triangle.
AW12 0176519637
Figure Number C07-F58-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F58 -AW12.ai
True. e.g., The diagonals are straight lines. Where two straight
lines cross, they always create two pairs of equal angles.
e.g., Hayley can use string or tape to mark the diagonals. The
diagonals will cross at the centre of the stage. OR Hayley
can mark the midpoint of each side and join each midpoint
to the opposite midpoint. The lines will cross in the centre of
the stage.
AW12 0176519637
Figure Number C07-F54-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F54 -AW12.ai
AW12 0176519637
Figure Number C07-F55-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F55 -AW12.ai
AW12 0176519637
Figure Number C07-F57-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F57 -AW12.ai
1. e.g.,
2. b) e.g.,
2. a) e.g.,
Chapter 7 Polygons 173NEL
07_AW12_Ch07.indd 173 1/9/12 10:42 PM
17NEL Chapter 7 Polygons
Pavithra uses regular polygons to make wooden trays. Which regular polygons are in this tray?
1 Find a triangle in this tray. Is it a regular polygon? Explain.
2 Name all the regular polygons in this tray.
Example 1Olivia designs and sells cloth potholders. To make the design at the right, she sewed a light-coloured hexagon on a dark-coloured hexagon. The dark hexagon is slightly larger. The light hexagon is a smaller similar polygon.
How can Olivia use a tracing of the dark hexagon to make a model of the light hexagon?
SolutionA. Mark the midpoint of each side. Draw
straight lines to join each midpoint to the next midpoint.
B. How do you know the shapes are similar?
Regular Polygons7.47.47.47.47.47.47.47.47.47.47.47.47.4Use six toothpicks. Create an irregular hexagon. Use six toothpicks. Create an irregular hexagon. How do you know that your hexagon is not regular? How do you know that your hexagon is not regular? Use a diagram to explain.Use a diagram to explain.
Try These
similar polygons
polygons that are congruent, or enlargements or reductions of each other; the ratios of corresponding sides are equal and the corresponding angles are equal
C07-F62-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
You will need• 6 toothpicks• a ruler• a protractor• a compass
No. e.g., Only two sides are equal.No. e.g., Only two sides are equal.
e.g., The interior angles are not equal.e.g., The interior angles are not equal.e.g., The interior angles are not equal.e.g., The interior angles are not equal.
square, octagon, pentagon, and hexagonsquare, octagon, pentagon, and hexagon
e.g.,
irregular
e.g., The original shape has six equal sides and equal interior e.g., The original shape has six equal sides and equal interior
1208 angles. The new shape also has these properties, but its angles. The new shape also has these properties, but its
side lengths are smaller.side lengths are smaller.174 Apprenticeship and Workplace 12 NEL
18 Apprenticeship and Workplace 12 NEL
C. Test these regular polygons. Does the midpoint reducing method always work to make a similar smaller polygon?
AW12 0176519637
Figure Number C07-F65-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F65-AW12.ai
AW12 0176519637
Figure Number C07-F66-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F66-AW12.ai
AW12 0176519637
Figure Number C07-F67-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F67-AW12.ai
D. Will all regular polygons have this property? Explain.• Joining the midpoints of each side of a regular polygon
creates a similar regular polygon.
Example 2Craig designs and makes signs in Regina. A customer wants a sign that is a regular pentagon.
How can Craig determine the angle measures for the sign?
SolutionA. Sketch a convex pentagon. It can be regular or irregular.
B. Draw diagonals from one vertex to divide your pentagon into triangles. How many triangles did you make?
C. What is the sum of all the interior angles of your pentagon?
(1808) 5
The sum is .
D. What angle measure should Craig use?
4 5 5
Craig should use .
ReflecTinGGabriel drew a
square. He says that all squares
are similar to the square he drew. Do you agree?
Explain.
ReflecTinGCan you always divide a shape into triangles to
determine its angle measures? Is
this a property of regular polygons?
Explain.
yes yes yes
Yes. e.g., The number of midpoints matches the number of
vertices, so the polygons are the same type. The distance
between the midpoints does not change, so both polygons
have equal sides. The angle from one midpoint to the next
does not change, so both polygons have equal angles.
AW12 0176519637
Figure Number C07-F68-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F68-AW12.ai
A. e.g.,
three
3 5408
5408
5408 1088
1088
Chapter 7 Polygons 175NEL
07_AW12_Ch07.indd 175 1/9/12 10:42 PM
19NEL Chapter 7 Polygons
Practice 1. Billy engraves names on ID bracelets. The bracelets are made
in these two shapes. Are they regular polygons? Explain.
a)
AW12 0176519637
Figure Number C07-F69-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F69-AW12.ai
b)
AW12 0176519637
Figure Number C07-F70-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F70-AW12.ai
2. Draw diagonals from one vertex of each shape to divide the shape into triangles. Use the triangles to complete the chart.
ReflecTinGAs the number of sides in a polygon
increases, the polygon looks more and more
like a circle. What happens to the interior angles?
Property
AW12 0176519637
Figure Number C07-F71-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F71 -AW12.ai
Hexagon
AW12 0176519637
Figure Number C07-F72-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F72 -AW12.ai
Heptagon
AW12 0176519637
Figure Number C07-F73-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F73 -AW12.ai
Octagon
Number of triangles
Sum of all the angle measures
Measure of each interior angle
Measure of each exterior angle
Sum of the measures of all the exterior angles
3. Use your chart from Question 2.
a) What happens to the number of triangles when you add one side to a polygon?
b) How many triangles can you make in a 12-sided polygon?
c) What size are the interior angles of a 12-sided regular polygon?
d) How does the number of triangles you can make in any polygon relate to the number of sides?
e) What is the measure of each angle in a regular decagon?
No. e.g., The interior angles are not equal. No. e.g., The sides are not equal.
4
7208
1208
608
3608
5
9008
128.571 …8
51.428 …8
3608
6
10808
1358
458
3608
It increases by 1.
10
1508
number of triangles 5 number of sides 2 2
(1808)(10 2 2) 4 10 5 1448
176 Apprenticeship and Workplace 12 NEL
07_AW12_Ch07.indd 176 1/9/12 10:42 PM
20 Apprenticeship and Workplace 12 NEL
4. Draw all the diagonals in each regular polygon. How many diagonals does each polygon have?
4 sides 5 sides 6 sides 7 sides
AW12 0176519637
Figure Number C07-F74-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F74 -AW12.ai
AW12 0176519637
Figure Number C07-F75-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F75 -AW12.ai
AW12 0176519637
Figure Number C07-F76-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F76-AW12.ai
AW12 0176519637
Figure Number C07-F77-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F77-AW12.ai
diagonals diagonals diagonals diagonals
5. Use the polygons in Question 4. Test the following properties of regular polygons. Decide whether each property is true or false.
a) If the number of vertices is odd, the number of diagonals is odd.
b) If the number of vertices is even, the diagonals that connect opposite vertices intersect at the centre.
c) The number of diagonals you can draw from one vertex of a regular polygon is n 2 3, where n is the number of vertices.
6. Regular octagons are often used for the Chinese New Year. The number 8 is associated with wealth and good luck.
C07-F79-AW12SB
CrowleArt Group
3rd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
The perspective was deleted.
a) Draw diagonals to join pairs of opposite vertices in this octagon. What is the measure of each angle where the diagonals meet?
b) What type of triangle do the diagonals make?
c) Place one end of a compass at the centre. Place the other end at a vertex. Draw a circle. What happens?
ReflecTinGWhich properties
of regular octagons are shared by all
regular polygons?
ReflecTinGUse one part in
Question 5 where you wrote “false” for the answer. Explain why it
is false.
2 5 9 14
false
true
true
3608 4 8 5 458
isosceles
The circle touches all the vertices.
Chapter 7 Polygons 177NEL
07_AW12_Ch07.indd 177 1/9/12 10:42 PM
21NEL Chapter 7 Polygons
Angela creates designs with floor tiles. To cover a floor with no gaps, the tiles must fit together so that the angle measures have a sum of 3608. Create a design that Angela could use.
1 Draw a design that could be made with floor tiles. Use at least two different polygons. The polygons must fit together so that the angle measures have a sum of 3608. Record angle measures with a sum of 3608.
ExampleJordan is a machinist in Yellowknife. This chart shows a method he uses to space bolt holes at equal distances around a circle.
How can Jordan use a regular pentagon to space five holes at equal distances around a wheel?
Applications of Polygons7.57.57.57.57.57.57.57.57.57.57.57.57.5Look around your classroom.Look around your classroom.i) Where do you see a polygon? Name this polygon. do you see a polygon? Name this polygon.
ii) Describe some Describe some properties of this polygon.
Try TheseYou will need• a millimetre ruler• a protractor• a compass
To get this many holes around a circle …
… multiply the diameter of the circle by the number below. The result is the side length of a regular polygon with vertices at the locations of the holes.
3 0.8660
4 0.7071
5 0.5878
6 0.5000
8 0.3827
10 0.3080
12 0.2588
C07-F80-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
360°
e.g., The top of e.g., The top of
my desk is a rectangle.my desk is a rectangle.my desk is a rectangle.my desk is a rectangle.e.g., It has two pairse.g., It has two pairs
of equal sides. The equal sides are parallel. All four interior of equal sides. The equal sides are parallel. All four interior of equal sides. The equal sides are parallel. All four interior of equal sides. The equal sides are parallel. All four interior
angles are right angles.angles are right angles.angles are right angles.angles are right angles.
e.g.,
120°
120°60°60°45°°
45°90°
45°45°
90°
90°
75°
120°75°
178 Apprenticeship and Workplace 12 NEL
22 Apprenticeship and Workplace 12 NEL
SolutionA. Use a compass to construct a circle. What is the diameter of
your circle?
The diameter of the circle is mm.
B. Use the chart. Multiply the diameter by the number for five holes. The product is the side length of a regular pentagon.
( mm)(0.5878) 5 mm
The side length is mm.
Practice 1. A machinist wants to space eight bolt holes at equal distances
around a wheel. The diameter of the wheel is 60 cm.
a) What regular polygon can the machinist use to locate the holes?
b) How long will the sides of the polygon be, to the nearest millimetre?
2. Elaine is looking at floor-tile designs. Each design is made by repeating a regular polygon. The polygon in each design is different.
a) What is one regular polygon that could be used to make a floor-tile design? Explain.
b) What is one regular polygon that could not make a tiling design? Explain.
ReflecTinGThe
measurements in this example
are given in millimetres. When would a machinist have to measure
much more precisely?
Use the charts inside the back cover for converting units.
Hint
24 mme.g.,
e.g., 40e.g., 40
e.g., 40e.g., 40
regular octagonregular octagon
(60 cm)(0.3827) 5 22.962 cm
The sides of the polygon will be about 230 mm long.
e.g., A square; the interior angle is 908, and (4)(908) 5 3608.
e.g., A regular octagon; the interior angle is 1358. Regular octagons do not fit
together so that the sum of the angle measures is 3608.
e.g., 23.512e.g., 23.512
e.g., 24e.g., 24
Chapter 7 Polygons 179NEL
23NEL Chapter 7 Polygons
3. Cameron is a painter in Cambridge Bay. He knows that 1 L of paint covers about 50 sq ft. How many litres of paint will Cameron need to buy for this attic wall?
a) Separate a polygon into triangles by drawing diagonals. Draw diagonals WU and WU and WU WT in the diagram of the wall. WT in the diagram of the wall. WT
b) What is the area of each triangle?
Triangle DimensionsTriangle Dimensions Area
nWST Base 5
Height 5Area 5
12
(base)(height)
512
(28.0 ft)(12.0 ft)
5
nWTU Base 5
Height 5
nWUV Base 5
Height 5
c) What is the total area of pentagon STUVW?STUVW?STUVW
d) How many litres of paint will Cameron need to buy?
4. Alex makes signs in Moose Jaw. The owner of a pie company wants a slice of pie on a circular sign. He wants each vertex of the triangle to be on the circle.
a) Find the midpoint of each side of the triangle at the left. Use a protractor. Draw a perpendicular line through each midpoint. Extend the perpendicular lines so they meet.
b) Place a compass where the lines meet. Use this as the centre. Draw the circle for the sign.
5. Triangles are useful for building bridges because they provide support. What are three other places you see triangles in construction or industry?
4. 4. 4.
12.0
ft
28.0 ft
T U
S W
V
9.0
ft
6.7 ft22.0 ft
For nWUV, use 9.0 ft as the base. Subtract 22.0 ft from 28.0 ft to get the height.
Hint
e.g., roofs of houses, hydro towers, cranes
168.0 sq ft 1 132.0 sq ft 1 27.0 sq ft 5 327.0 sq ft
The total area is 327.0 sq ft.
327 sq ft 4 50 sq ft/L 5 6.54 L
He will need to buy 7 L.
1
2(base)(height) 5
1
2(9.0 ft)(6.0 ft)
5 27.0 sq ft
1
2(base)(height) 5
1
2(22.0 ft)(12.0 ft)
5 132.0 sq ft
28.0 ft
168.0 sq ft168.0 sq ft
22.0 ft
9.0 ft
12.0 ft
6.0 ft
12.0 ft
180 Apprenticeship and Workplace 12 NEL
24 Apprenticeship and Workplace 12 NEL
1. Circle the polygons.
AW12 0176519637
Figure Number C07-F86-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F86-AW12.ai
2. Name the quadrilaterals in Question 1.
3. Name the regular polygons in Question 1.
4. Sketch a polygon that has each property below. Classify each polygon.
a) Each interior angle is 608.
b) There are five equal sides.
5. Look at the polygons in the photographs at the right. One of the polygons has this property:• You can draw a line through the polygon so that the line
is parallel to the base to create a smaller polygon. The original polygon and the smaller polygon are similar.
Which polygon has this property? Explain. Include drawings.
chapter
square, parallelogram, rectangle, concave quadrilateral, and trapezoid
square and regular pentagon
equilateral triangle
e.g., regular pentagon
AW12 0176519637
Figure Number C07-F91-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F91-AW12.ai
shortersidelengths
same sidelength asoriginalrectangle
60°
60°
60°
AW12 0176519637
Figure Number C07-F87-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F87-AW12.ai
4. a) e.g.,
AW12 0176519637
Figure Number C07-F89-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F89-AW12.ai
4. b) e.g.,
e.g.,
The triangle has this property. e.g., Drawing a line through the triangle gives a smaller
triangle with the same angles. The triangles are similar. When you draw a line through
the rectangle, you get smaller rectangles. One side is equal to a side in the original
rectangle; the other side is not. The rectangles are not similar.
AW12 0176519637
Figure Number C07-F90-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F90-AW12.ai
sharedangle
same angles in both triangles
Chapter 7 Polygons 181NEL
07_AW12_Ch07.indd 181 1/9/12 10:43 PM
25NEL Chapter 7 Polygons
6. Is each property true or false? Draw a diagram on plain paper to show your answer.
a) If some interior angles of a polygon are equal, some exterior angles are equal.
b) If a polygon has equal angles, it also has parallel sides.
c) Increasing the number of sides in a regular polygon decreases the measure of the interior angles.
7. Ryan is a landscaper in Brandon. He is going to sod a lawn in the shape of quadrilateral PQRS at the left.
a) What is the area that Ryan will cover with sod?
b) What property of polygons did you use to solve the problem in Part a)?
8. Kylie designs and sews quilts. Describe a property of polygons that she might use in a quilt. Include a diagram with your description.
AW12 0176519637
Figure Number C07-F98-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F98-AW12.ai
50 ft15 ft
50 ftP
S R
Q
True. e.g., When you add the interior angle and exterior angle
at a vertex, the sum is always 1808. If two interior angles are
equal, then the corresponding exterior angles are equal.
False. e.g., An isosceles triangle has equal angles but no
parallel sides.
False. e.g., As the number of sides increases, the angle
measure also increases.
e.g., When you join the midpoints of the sides of a regular
polygon, you get a smaller similar polygon.
e.g., If you draw a diagonal in a quadrilateral, you get two triangles.
e.g., AreanQRS
5 1
2 (50 ft)(50 ft)
5 1250 sq ft
AreanPQS
5 1
2 (50 ft)(15 ft)
5 375 sq ft
1250 sq ft 1 375 sq ft 5 1625 sq ft
Ryan will cover an area of 1625 sq ft with sod.
AW12 0176519637
Figure Number C07-F92-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F92-AW12.ai
AW12 0176519637
Figure Number C07-F93-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F93-AW12.ai
60°
AW12 0176519637
Figure Number C07-F94-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F94-AW12.ai
AW12 0176519637
Figure Number C07-F95-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F95-AW12.ai
90°
AW12 0176519637
Figure Number C07-F96-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F96-AW12.ai
120°
6. a) e.g.,
6. b) e.g.,
6. c) e.g.,
AW12 0176519637
Figure Number C07-F100-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F100-AW12.ai
8. e.g.,
182 Apprenticeship and Workplace 12 NEL
07_AW12_Ch07.indd 182 1/9/12 10:43 PM
26 Apprenticeship and Workplace 12 NEL
1. Make a triangle by joining three cities on the map.
a) What are the side lengths of your triangle, in millimetres?
b) What are the angle measures of your triangle?
c) What are two names for the type of triangle you made?
d) What is one property that your triangle shares with all triangles?
e) What is one property that your triangle does not share with some triangles?
2. Draw a rectangle by joining Yellowknife, Baker Lake, Churchill, and Fort McMurray.
a) What are the side lengths, in millimetres?
b) What are the angle measures?
c) What are two names for the quadrilateral you made?
d) What is one property that this quadrilateral shares with another type of quadrilateral? Use diagrams.
Chapter
C07-F101-AW12SB
CrowleArt Group
2nd pass
AW12SB
0176519637
FN
CO
Technical
Pass
Approved
Not Approved
Iqaluit
Edmonton
Halifax
Regina
Whitehorse
Winnipeg
Churchill
BakerLakeYellowknife
FortMcMurray
Charlottetown
Moncton
St. John’sFredericton
Toronto
QuébecCity
Ottawa
Victoria
N
0 1000 km500
e.g., 1308, 308, and 208
18 mm, 18 mm, 11 mm, and 11 mm
e.g., obtuse triangle and
scalene triangle
e.g., It does not have equal sides or equal angles.
e.g., 16 mm, 20 mm, and 34 mm
e.g., The sum of
the interior angles is 1808.
908
rectangle and parallelogram
e.g., It has four right angles, like a square. OR When you
draw a diagonal in a rectangle, you always get two
congruent triangles. A rhombus has the same property.
AW12 0176519637
Figure Number C07-F102-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F102-AW12.ai
2. d) e.g.,
AW12 0176519637
Figure Number C07-F103-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F103-AW12.ai
Chapter 7 Polygons 183NEL
07_AW12_Ch07.indd 183 1/9/12 10:57 PM
27NEL Chapter 7 Polygons
e) What is one property that other quadrilaterals have, but this quadrilateral does not have? Use diagrams.
3. Claude says that a polygon is a regular polygon if all of its sides are equal. Do you agree? Include a diagram.
4. a) Describe and illustrate two properties of regular decagons. Include diagrams.
b) Describe one property that some other regular polygons have, but a regular decagon does not have. Include diagrams.
5. Andy is paving a walkway in Airdrie. He is using stones that are regular polygons, but they are different shapes.
Can he use the three shapes at the right to pave the walkway without leaving gaps between the stones? Explain.
6. Melissa is installing a square skylight. She does not have a protractor. How can she check that the hole she cut for the skylight is a square?
AW12 0176519637
Figure Number C07-F108-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F108-AW12.ai
No. e.g., A polygon can have equal sides and different
interior angles. To be regular, a polygon must have equal sides
and equal interior angles.
e.g., All the interior angles measure 1448. If you join
opposite vertices, all the diagonals cross in the centre.
e.g., An equilateral triangle has acute interior angles, but a
regular decagon does not.
Yes. e.g., The side lengths are equal.
The stones fit together so that the
sum of the angle measures is 3608: 608 1 1208 1 908 1 908 5 3608.
e.g., She can measure the four side lengths and the diagonals. If the hole
is square, the side lengths will be equal and the diagonals will be equal.
AW12 0176519637
Figure Number C07-F109-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F109-AW12.ai
e.g., A trapezoid has two different angles, but the angles
in my rectangle are all equal. OR If you extend the sides
of a trapezoid, you get a triangle. My rectangle does not
have this property.
3. e.g.,
4. a) e.g.,
4. b) e.g.,
5. e.g.,
2. e) e.g.,
AW12 0176519637
Figure Number C07-F105-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F105-AW12.ai
AW12 0176519637
Figure Number C07-F104-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F104-AW12.ai
AW12 0176519637
Figure Number C07-F106-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F106-AW12.ai
AW12 0176519637
Figure Number C07-F112-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F112-AW12.ai
144°
AW12 0176519637
Figure Number C07-F107-AW12.ai
Company MPS
Technical
Pass 1st pass
Approved
Not Approved
C07-F107-AW12.ai
Angles are
all 60°.Angles are
all 144°.
184 Apprenticeship and Workplace 12 NEL
07_AW12_Ch07.indd 184 1/9/12 10:43 PM
28 Apprenticeship and Workplace 12 NEL
Title ISBN Price
Nelson Mathematics for Apprenticeship and Workplace 10
Workbook (5-Pack) 9780176514303 $89.95
Solutions—Print 9780176504052 $49.95
Solutions—CD-ROM (non-printable) 9780176505080 $49.95
Computerized Assessment Bank 9780176515249 $299.95
Nelson Mathematics for Apprenticeship and Workplace 11
Workbook (5-Pack) 9780176514297 $89.95
Solutions—Print 9780176504175 $49.95
Solutions—CD-ROM (non-printable) 9780176508937 $49.95
Computerized Assessment Bank 9780176515232 $299.95
Nelson Mathematics for Apprenticeship and Workplace 12—coming May 2012
Workbook (5-Pack) 9780176519612 $114.95
Solutions—Print 9780176519643 $79.95
Solutions—CD-ROM (non-printable) 9780176519629 $79.95
Computerized Assessment Bank 9780176519605 $299.95
Prices are subject to change without notice.
[email protected] web: www.nelsonschoolcentral.com
Order by phone1-800-268-2222
Order by fax1-800-430-4445
Order by emailNelson Education 1120 Birchmount Road Toronto, ON M1K 5G4
Order by mailNelson Mathematics for Apprenticeship and Workplace Order Information
Sales RepresentativesBritish Columbia/YukonJill Nessel, Regional Manager(780) 416-8660 1-800-668-0671, Ext. 5565Fax: 1-800-430-4445email: [email protected]
Abbotsford 34, Chilliwack 33, Conseil scolaire francophone 93, Delta 37, Distance Education 101, Langley 35, Maple Ridge-Pitt Meadows 42, Mission 75, New Westminster 40, Powell River 47, Richmond 38, Sea to Sky 48, Sunshine Coast 46, Vancouver 39, Yukon
Lynda Parmelee, Territory Manager(778) 285-4418 1-800-668-0671, Ext. 5510Fax: 1-800-430-4445 email: [email protected]
Alberni 70, Burnaby 41, Campbell River 72, Comox Valley 71, Coquitlam 43, Cowich Valley 79, Greater Victoria 61, Gulf Island 64, Nanaimo-Ladysmith 68, North Vancouver 44, Qualicum 69, Saanich 63, Sooke 62, Surrey 36, Vancouver Island North 85, Vancouver Island West 84, West Vancouver 45
Randy Arduini, Territory Manager(604) 464-1515 1-800-668-0671, Ext. 2250 Fax: 1-800-430-4445email: [email protected]
Arrow Lakes 10, Boundary 51, Bulkley Valley 54, Cariboo-Chileotin 27, Central Coast 49, Central Okanagan 23, Coast Mountains 82, Fort Nelson 81, Fraser-Cascade 78, Gold Trail 74, Haida Gwaii/Q Charlotte 50, Kamloops/Thompson 73, Kootenay Columbia 20, Kootenay Lake 8, Nechako Lakes 91, Nicola-Similkameen 58, Nisga’a 92, North Okanagan-Shuswap 83, Okanagan Similkameen 53, Okanagan Skaha 67, Peace River North 60, Peace River South 59, Prince George 57, Prince Rupert 52, Quesnel 28, Revelstoke 19, Rocky Mountain 6, Southeast Kootenay 5, Stikine 87, Vernon 22Jennifer Dow, Territory Manager1-800-668-0671, Ext. 7222 (778) 476-5901 Fax: 1-800-430-4445email: [email protected]
AlbertaJill Nessel, Regional Manager(780) 416-8660 1-800-668-0671, Ext. 5565Fax: 1-800-430-4445email: [email protected]
Aspen View, Battle River, Black Gold, Edmonton Public, Edmonton Catholic, Elk Island Catholic, Elk Island Public, Evergreen Catholic, Fort McMurray, Fort McMurray Catholic, Fort Vermillion, Grande Prairie Roman Catholic, Grande Prairie Public, Grande Yellowhead, Greater St. Albert Catholic, High Prairie, Holy Family Catholic, Lakeland Roman Catholic, Living Waters Catholic, Northern Gateway, Northern Lights, Northland, Parkland, Peace River, Peace Wapiti, Pembina Hills, St. Albert Protestant, St. Paul, St. Thomas Aquinas Roman Catholic, Sturgeon
Carla Bergmann, Territory Manager(780) 292-1665 1-800-668-0671, Ext. 5620 Fax: 1-800-430-4445email: [email protected]
Buffalo Trail, Calgary Public, Calgary Roman Catholic, Canadian Rockies, Chinook’s Edge, Christ the Redeemer Catholic, Clearview, East Central Alberta Catholic, Foothills, Golden Hills, Grasslands, Holy Spirit Roman Catholic, Horizon, Lethbridge, Livingstone Range, Medicine Hat, Medicine Hat Catholic, Palliser, Prairie Land, Prairie Rose, Red Deer, Red Deer Catholic, Rocky View, Wetaskiwin, Wild Rose, Wolf Creek
Roger Laycock, Territory Manager(403) 998-3911 1-800-668-0671, Ext. 5506(403) 275-7076 Fax: 1-800-430-4445email: [email protected]
Saskatchewan, NWT, NunavutJill Nessel, Regional Manager(780) 416-8660 1-800-668-0671, Ext. 5565Fax: (780) 467-9079email: [email protected]
Territory Manager TBD
ManitobaJill Nessel, Regional Manager(780) 416-8660 1-800-668-0671, Ext. 5565 Fax: 1-800-430-4445email: [email protected]
Lewis Minuk, Territory Manager(204) 694-9877 Fax: 1-800-430-4445email: [email protected]
Kerry Kuran, Territory Manager(204) 253-4941Fax: 1-800-430-4445email: [email protected]
Ron Westcott, Territory Manager(204) 832-7177Fax: 1-800-430-4445email: [email protected]
Comprehensive supplementary workbooks!Nelson Mathematics for Apprenticeship and Workplace 10–12 is a series of comprehensive supplementary workbooks, carefully designed to engage students in the real-life contexts of mathematics.• Written at an appropriate reading level• Supports 100% of the outcomes in the curriculum• Each lesson includes prompts, examples, and
exercises scaffolded in manageable steps• Consistent, easy-to-follow layout
9 780176 539979
ISBN-10: 0-17-653997-2ISBN-13: 978-0-17-653997-9
01/12
Nelson Mathematics for Apprenticeshipand Workplace 10–12
To learn more about Nelson Education’s new secondary math resources visit www.nelson.com/wncpmath
NEW!
1120 Birchmount Road Toronto ON M1K 5G4
416 752 9448 or 1 800 268 2222 Fax 416 752 8101 or 1 800 430 4445
email: [email protected] www.nelsonschoolcentral.com
See inside back cover for ordering
information.
Also from Nelson Education: