Geometry and Measurement

What You Will Learn To draw a line segment parallel to another line segment To draw a line segment perpendicular to another line segment To draw a line that divides a line segment in half and is

perpendicular to it To divide an angle in half To develop and use formulas to calculate the area of triangles

and parallelograms.

CHALLENGE Try to draw what the what you think the first 5 bullets may

look like.

What You Will Need

• Geometry Set– Ruler– Protractor – Right Triangle

• Pencil• Textbook

ReviewLine Segment: the part of a line between 2 end points.Line: a line segment with no end points

3.1 Parallel and Perpendicular Line Segments After this lesson you will be able to…

Draw line segments that are parallel to each other

Draw line segments that are at right angles to each other.

What Are Line Segments? Parallel Line Segments

Describes lines in the same plane that never cross, or intersect

They are marked using arrows The perpendicular distance between

line segments must be the same at each end of the segment.

To create, use a ruler and a right triangle, or paper folding

Parallel sides

Lesson 1Students will be able to describe different shapes

Learn Albertahttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html

Parallel: two lines or two sides that are the same distance apart and never meet.

Arrows: show parallel sides

Vertex: the point where sides meet or intersect

Lesson 1Students will be able to describe different shapes

Learn Alberta - parallelhttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html

Parallel: two lines or two sides that are the same distance apart and never meet.

Arrows: show parallel sides (where do the arrows go below)?

Vertex: the point when sides meet or intersect

PAGE 84

• Let’s us draw parallel line segments

• Try to draw and check your drawings.

What Are Line Segments?

Perpendicular Line Segments Describes lines that intersect at right angles (90°) They are marked using a small square To create use a ruler and a protractor,

or paper folding.

Perpendicular: where a horizontal edge and vertical edge intersect to form a right angleOR

when two sides of any shape intersect to make a right angle

Right Angle: 90’ symbol is a box in the corner

Vertical

Horizontal

Learn Alberta - Perpendicularhttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Perpendicular/index.html

Vertical side

Perpendicular side

Perpendicular side

Perpendicular: where a horizontal edge and vertical edge intersect to form a right angle

OR when two sides of any shape intersect to make a right angle

Right Angle: 90’ symbol is a box in the corner

How many perpendiculars do you see in each diagram

Perpendicular: where a horizontal edge and vertical edge intersect to form a right angle

Right Angle: 90’ symbol is a box in the corner

How do you describe a perpendicular using points

OnYour Own…

What are 5 examples of parallel line segments in the real world?

What are 5 examples or perpendicular line segments?

PAGE 85

• Let’s us draw perpendicular line segments

• Try to draw and check your drawings.

Practice Pg 87. #5 What are the parallel and perpendicular line

segments in the painting.

Practice Pg 87. #5 What are the parallel and perpendicular line

segments in the painting.

Segments CD, EF, and GH are parallel. AB is perpendicular to CD, EF, and GH.

Practice Identify the parallel and perpendicular streets

in the diagram.

Practice Identify the parallel and perpendicular streets

in the diagram.Major Street and CentreStreet are parallel Main Street and North Streetare parallel. Major Street is perpendicularto Main Street and NorthStreet. Centre Street is perpendicular to Main Street and North Street.

On Your Own…

• Page 87

Practice and Apply #7, 9, 10, 12, 13, Extend #15, 16

3.2Draw Perpendicular Bisectors

What is A Perpendicular Bisector? On your rice paper:

Use a ruler to draw a 15 cm line segment Label the endpoints A and B. Fold the piece of paper so that the points A and B lie on

top of each other. Use a ruler to draw a line segment on the crease. Label

this line segment CD. Label the point where the two line segments intersect P.

Use a ruler to measure lengths AP and BP. What do you notice?

Use a protractor to measure the 4 angles made by the intersecting line segments. What do you notice about these angles.

What is a Perpendicular Bisector??

• A Perpendicular Bisector:– Is a line segment in half and is at right angles (90°)

to the line segment.

Example• Pg. 93, #9• In some First Nations communities, fish are dried on a

drying rack like the one shown. An extra support is needed for this drying rack to hold all the salmon that were caught. Use what you know about drawing perpendicular bisectors to explain how to do this. Include the lengths shown

in the picture in your explanation

Solution• Cut a support post that is 1.4 m long. To find the halfway

point of the top horizontal pole, divide the length of 3 m in half to get 1.5 m. Place the support at this halfway point. Measure a right angle where the top pole and the support meet in order to position the support perpendicular to the top pole.

Let’s PracticePg. 92 #4- Trace the lines onto your rice paper. Use your

protractor to measure the correct angles #6, 7, 8, 10

Due Tomorrow for Homework!!

3.3 Draw Angle Bisectors

3.3 Draw Angle Bisectors

http://www.freewebs.com/mrsdeleon/mathlinks.htm#Geometry

What Will I Learn??

To draw a line that divides a line segment in half and is perpendicular to it

To divide an angle in half

Lesson #3Student Outcome: I will be able to understand perimeter.

How much fence will you need to enclose this baseball field?

Lesson #3Student Outcome: I will be able to understand perimeter.

Perimeter: the distance around a shape

or

the sum of all the sides

Lesson #3Student Outcome: I will be able to understand perimeter.

How can you figure out these perimeters?

Lesson #3Student Outcome: I will be able to understand perimeter.

You need a tarp to cover this soccer field. How do you figure this out?

Lesson #3Student Outcome I will be able to understand perimeter and area.

Area: the amount of surface a shape covers : it is 2-dimensional - length (l) and width (w)

: measured in square units (cm ²) or (m²)

Lesson #3Student Outcome: I will be able to understand perimeter and area.

Figure the area for these objects?

6cm

8 cm50 cm

100 cm

46 cm

183 cm

Lesson #3Student Outcome: I will be able to understand perimeter and area.

Figure the perimeter for these objects?

6cm

8 cm50 cm

100 cm

46 cm

183 cm

Lesson #3Student Outcome: I will be able

to understand perimeterand area.

What are the perimeters for each rectangle?

What are the areas for each rectangle?

What do you notice?

Length Width Area Perimeter

Page 128

Lesson #3Student Outcome: I will be able

to understand perimeter and area.

Page 129

Length Width Area Perimeter

8 cm²

14cm² 18cm² 20cm²

What did we find out?

Lesson #3Student Outcome: I will be able

to understand perimeter and area.

Page 129

Length Width Area Perimeter

8 cm²

14cm² 18cm² 20cm²

What did we find out?

The rectangles with the least width has the least area.

The rectangle closest in shape to a square has the greatest area.

Lesson #3Student Outcome: Student Outcome: I will be able to understand perimeter and area.

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=12

Area and Perimeter Video ( Learn Alberta)

What is an Angle Bisector??

An angle bisector is a line that divides the angle evenly in terms of degrees.

The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. To help us make this distinction, look at our picture of a rectangular backyard. The yard is 2-dimensional: it has a length and a width. The amount of fence needed to enclose the backyard (perimeter) is 1-dimensional. The perimeter of this yard is the distance around the outside of the yard, indicated by the red arrow; It is measured in linear units such as feet or meters.

PERIMETER

To find the perimeter of a polygon, take the sum of the length of each side. The polygons below are much smaller than a fenced-in yard. Thus, we use smaller units in our examples, such as centimeters.

Area of a rectangle or square

Area = length x width

A = l x w

Area of a parallelogram

Area = base x height

A = b x h

Area of a triangle

Area = (base x height) ÷ 2

Area = (b x h) ÷ 2

http://www.calfeedesign.com/index.htm

http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Bicycle_Frame_Diagram-en.svg/443px-Bicycle_Frame_Diagram-en.svg.png