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Chapter 1: Tools of Geometry
Chapter 1 – Day 1 – Points, Lines and Planes
Objectives: SWBAT identify Points, Lines, Rays, and Planes.
SWBAT identify Coplanar and Non-Coplanar Points.
Point The basic unit of Geometry. It is a location
Line
An infinite series of points extending in two opposite directions. Any two points make a line
Plane A flat surface that extends in all directions without end.
Any three points not the same line make a plane
A Written as
A
m
A
B
P Q
RS
Written as
plane PQRS plane QRSP
plane RSPQ plane SPQR
B D
C
k
Written as
plane DBC plane DCB
plane CDB plane CBD
plane BDC plane BCD
plane K
or
Written as
AB BA or line m
n
A
C
E
D
F
H
B
Collinear
Points that lie on the same line.
Non-Collinear
Points that do not lie on the same line. Must include at least three points
Coplanar Points, lines, segments, or rays that lie on the same plane.
Examples
1. What is another name for ?
Any of the following
2. Give two other names for plane n.
As long as they are any 3 non-collinear points
3. Explain why ABC is not proper way to name plane n.
They are on the same line, a plane is defined as three points NOT on the same line or three non-collinear points
4. Tell whether or not the sets are collinear. If so, why or why not.
a. B and F b. BD and E
Yes, any two points make a line Yes, A line extends out forever, and
includes point E as it keeps going
c. EB and A d. plane n and F.
No, A does not lie on the line so No, a plane is made up of 3 non-collinear it cannot be collinear points so by definition it false
, , , ,BD DE ED EB AB
, , ,plane ADB plane BAE plane CBD ect
BD
Refer to the following figure.
5. How many planes are in the figure?
Exactly 5
6. Name three planes.
Plane ABC, Plane ABF, Plane CDFE, Plane DLF, Plane ECA, ect.
7. Name three collinear points.
A, H, and B or B, L, and F
8. Are the points A, H, L and D coplanar? Explain.
No, only A, H, and L lie on the same plane, D is on another plane No plane can be made using all four of those points.
9. Are the points B, D, and F coplanar? Explain.
Yes, all three points lie on the same plane. Three non-collinear points make a plane.
10. Nathan’s Mother wants him to go to the post office and the
supermarket. She tells him that the post office, the supermarket, and their home are collinear. If the post office is between the supermarket
and their home; make a map showing the three locations based on this information.
A
B
C
D
E
F
H L
Chapter 1 - Day 2 – Points, Lines, Planes
Objectives: SWBAT construct Points, Lines, Rays, and Planes.
Construction
To create a geometric concept using points, lines, segments, and angles. Examples:
No because they are not all on the same plane.
6
, ,S X M
Chapter 1 - Day 3 – Linear Measure
Objectives: SWBAT measure segments
SWBAT calculate with measures
Line Segment Part of a line with a definite beginning and end.
Line Segment Measure
The measurement or length of a line segment
If you are talking about a segment’s length then NO HAT. If you are
talking about a segment in general terms it HAS A HAT.
Congruence
Having the exact same measurement
Congruent Segments Segments that have the exact same measurement
Also can be shown by using tick marks
A B
or
Written by
AB BA
0
1
2
M
N
Written by
MN or NM
Written with
A B
C D
Written as
AB CD
A B
C D
Segment Addition Postulate
A segment can be accurately measured by the sum of its parts. Add up all the
pieces to make a whole
Whole segment = Parts added together
Notice that AB and BC are NOT always congruent, and should NOT be assumed to be congruent unless specified.
Examples:
1. If AB = 3 cm, and BC = 11 cm, find AC.
2. Find YZ.
A B C
AC
AB BC
Whole Sum of the Parts
AB BCAC
A B C
X
Y
Z
32 mm
15 mm
3 11
14
AC AB BC
AC
AC cm
32 15
17
XZ XY YZ
YZ
mm YZ
3. If MO = 32, find the value of each of the following.
a. x =______
Find x first, then we will be able to find the segment measurements.
Then we plug “x” back into each given segment
b. MN = _________
c. NO = _________
4. Suppose J is between H and K. Find the length of each segment.
HJ= 2x + 4
JK= 3x + 3
KH= 22
Draw a picture 1st, which will be very helpful.
Label your picture second.
Third, Write your equation and solve for x
Lastly, Plug x back into the given information
32 3 16
32 4 16
16 4
4
MO MN NO
x x
x
x
x
3
3(4)
12
MN x
MN
MN
16
(4) 16
20
NO x
NO
NO
H J K
22 2 4 3 3
22 5 7
15 5
3
HK HJ JK
x x
x
x
x
2 4
2(3) 4
10
HJ x
HJ
HJ
3 3
3(3) 3
12
JK x
JK
JK
H J K
2x+4 3x+3
22
5. In the diagram below, 𝑀𝑄 = 30, 𝑀𝑁 = 5, 𝑀𝑁 = 𝑁𝑂, and 𝑂𝑃 = 𝑃𝑄.
Which of the following statements is not true?
A. 𝑁𝑃 = 𝑀𝑁 + 𝑃𝑄 C. 𝑀𝑄 = 3 ∙ 𝑃𝑄
B. 𝑀𝑃 = 𝑂𝑄 D. 𝑁𝑄 = 𝑀𝑃
First always label your diagram Second – if you can, solve for all the segments
6. Given the following diagram, find the length of GK given that GH HK .
Since the segments are congruent,
you can set them equal to each other and solve for x.
Since it has an 𝒙𝟐 you need to set Distance can never be negative so it equal to zero and factor / the answer of – 6 can’t work. quadratic formula.
30 5 5
30 10 2
20 2
10
MQ MN NO OP PQ
x x
x
x
x
2 18 3
GH HK
x x
2
2
18 3
3 18 0
6 3 0
6 3
x x
x x
x x
x x
2
2
3
18 3
3 18 3 3
9 18 9
18
x
GK GH HK
GK x x
GK
GK
GK
7. Jorge used the figure at the right to make a pattern for a mosaic he plans to inlay on a tabletop. Name all the congruent segments in the figure.
Segments with the same number of tick marks are congruent.
1 Tick Mark
FE BC
2 Tick Marks
FA AB ED DC
Chapter 1 – Day 4 – Distance Formula
Objectives: SWBAT find the distance between two points
Distance
The length between two points, or the length of a segment with two distinct endpoints
Distance on a number-line Distance on a Coordinate Plane
Distances must always be a positive number.
Examples
1. Use the number line to find distance of each segment
A) XY B) WZ C) YW
2 1 1 2| | | |PQ x x or x x
P Q
1x 2x
2 2
2 1 2 1PQ x x y y
P
Q
1 1( , )x y
2 2( , )x y
-6 -5 -1-2-3-4 0 1 2 3 4 5 6 7 8
W X YZ
2 1| |
| 7 1 |
| 8 |
8
XY x x
XY
XY
XY
2 1| |
| 4 5 |
| 9 |
9
WZ x x
WZ
WZ
WZ
2 1| |
| 5 7 |
| 12 |
12
YW x x
YW
YW
YW
2. Find the distance of the following segments.
AB
A = 1st point = 1 1,x y
B = 2nd point = 2 2,x y
AC
A = 1st point = 1 1,x y
C = 2nd point = 2 2,x y
Find the distance between the Find the missing part of the endpoint following points
3. 3,5 , 3,13P Q 4. 𝑫 = 𝟓 𝒊𝒏. 𝑨 (𝟑, 𝟐) 𝑩 (𝟕, 𝒚𝟐)
A
B
C
2 2
2 1 2 1
2 2
2 2
2 3 3 9
1 12
1 144
145
AB x x y y
AB
AB
AB
AB
2 2
2 1 2 1
2 2
2 2
9 3 0 9
6 9
36 81
117
AC x x y y
AC
AC
AC
AC
2 2
2 1 2 1
2 2
2 2
3 3 13 5
6 8
36 64
100
10
PQ x x y y
PQ
PQ
PQ
PQ
PQ
2 2,x y 1 1,x y
2 2
2 1 2 1
2 2
2
2 2
2
2
2
22 2
2
2
2
2
2
2
2
2
2
5 7 3 2
5 4 2
5 16 2
5 16 2
25 16 2
9 2
9 2
3 2
5
D x x y y
y
y
y
y
y
y
y
y
y
2 2,x y 1 1,x y
1. Paul and Susan are standing outside City Hall. Paul walks three blocks north and two blocks west while Susan walks five blocks south and fourth blocks east.
If city Hall represents the origin, find the distance of Paul and Susan’s new locations.
2 2
2 1 2 1
2 2
2 2
2 4 3 5
6 8
36 64
100
10
d x x y y
d
d
d
d
d
Chapter 1 – Day 5 – Midpoint Formula
Objectives: SWBAT find the midpoints between two points
SWBAT find the endpoint of a segment given a midpoint
Midpoint
The point halfway between two endpoints.
Midpoint on a Line Midpoint on a Coordinate Plane
The mean or average of the two points
Examples
1. Use the number line to find midpoint of each segment
A) XY B) WZ
1 2
2
x xM
1 2 1 2,2 2
x x y yM
P
QM
2 2( , )x y
1 1( , )x y
1 2 1 2,2 2
x x y y
A BM
1x 2x1 2
2
x x
-6 -5 -1-2-3-4 0 1 2 3 4 5 6 7 8
W X YZ
1 2
2
1 7
2
6
2
3
x xM
M
M
M
1 2
2
5 4
2
1
2
1
2
x xM
M
M
M
2. Find the midpoint of MN , M = ( 1 , 4 ) and N = ( 7, 6 ).
M = 1st point = 1 1,x y
N = 2nd point = 2 2,x y
Find the midpoint between the following points.
3. 3,5 , 3,13A B 4. 4, 7 , 0,15A B
5 – Find the coordinates of A if B = ( 10 , 8) and the midpoint of AB = ( 7 , 10 ).
A = 1st point = 1 1,x y
B = 2nd point = 2 2,x y
Midpoint = ,m mx y
1 2 1 2,2 2
1 7 4 6,
2 2
8 10,
2 2
4, 5
4,5
m m
m m
m m
m m
x x y yx y
x y
x y
x y
1 2
1
1
1
2
107
2
14 10
4
4,12
m
x xx
x
x
x
1 2
1
1
1
2
810
2
20 8
12
m
y yy
y
y
y
2 2,x y 1 1,x y 2 2,x y 1 1,x y
1 2 1 2,2 2
3 3 5 13,
2 2
0 18,
2 2
0, 9
0,9
m m
m m
m m
m m
x x y yx y
x y
x y
x y
1 2 1 2,2 2
4 0 7 15,
2 2
4 8,
2 2
2, 4
2,4
m m
m m
m m
m m
x x y yx y
x y
x y
x y
Find the coordinates of the missing endpoint if E is the midpoint of DF.
6. 𝑫(−𝟑, −𝟖), 𝑬(𝟏, 𝟐) 7. 𝑭(𝟓, 𝟏𝟏), 𝑬 (𝟓
𝟐, 𝟔)
8 - In the figure, B is the midpoint of AC , find the value of b.
Midpoint implies congruence or equal measure. Set it equal to each other and solve.
Segment Bisector
A segment, plane or line that cuts a segment
in half, or intersects a segment at its midpoint.
A B C
3 4b 5b
3 4 5
4 2
2
b b
b
b
,m mx y 1 1,x y
1 2
2
2
2
2
31
2
2 3
5
m
x xx
x
x
x
1 2
2
2
2
2
82
2
4 8
12
m
y yy
y
y
y
5,12
,m mx y 1 1,x y
1 2
2
2
2
2
55
2 2
5 5
0
m
x xx
x
x
x
0,1
1 2
2
2
2
2
116
2
12 11
1
m
y yy
y
y
y
9 – In the figure, EF is a bisector of HG , find x.
Bisector bisects or cuts in half. Set the two segments equal to each other and solve.
10. Paul and Susan are standing outside City Hall. Paul walks three blocks north and two blocks west while Susan walks five blocks south and fourth blocks east. If City Hall represents the origin, find the midpoint of Paul and Susan’s new locations.
1 2 1 2,2 2
2 4 3 5,
2 2
2 2,
2 2
1, 1
1, 1
m m
m m
m m
m m
x x y yx y
x y
x y
x y
E
F
GH 2 5x
7x 7 2 5
12
x x
x
Chapter 1 – Day 6 – Partitioning a Segment
Objectives: SWBAT find a point on a line segment between two given points that divides into a specific ratio:
Partition: To break a segment into smaller pieces Based on a specific ratio.
Ratio:
A fraction, or parts of a whole
Break the following segments into the ratios. 1. 3 to 2
2. 4 to 6
3. 3 to 5
4. 3 to 1
,LEFT x y
,RIGHT x y
1. Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 1.
Ratio: Mental Picture of Ratio
2. Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 7. Given that A( –2, –10) and B(8, 10).
Ratio: Mental Picture of Ratio
3:1
3
4
Ratio
Distance
8 8
16
316
4
3 16
4 1
12
12
8 12
4
x
units
Move Units to the Right
x Coordinate
Distance
7 5
12
312
4
3 12
4 1
9
9
7 9
2
y
units
Move Units Up
y Coordinate
4,2
Answer
3: 7
3
10
Ratio
Distance
2 8
10
310
10
3 10
10 1
3
3
2 3
1
x
units
Move Units to the Right
x Coordinate
Distance
10 10
20
320
10
3 20
10 1
6
6
10 6
4
y
units
Move Units Up
y Coordinate
1, 4
Answer
3. Find the coordinates of P along the directed line segment AB so that the ratio of
AP to PB is 2 to 3. Given that 𝑨(𝟗, 𝟒) and 𝑩(−𝟏, 𝟐).
Ratio: Mental Picture of Ratio
2 : 3
2
5
Ratio
Distance
1 9
10
210
5
2 10
5 1
4
4
1 4
3
x
units
Move Units to the Right
x Coordinate
Distance
2 4
2
22
5
2 2
5 1
4
5
4
5
42
5
14 2.8
5
y
units
Move Units Up
y Coordinate or
143,
5
Answer
4. An 80 mile trip is represented on a gridded map by a directed line segment from
point 𝑴(𝟑, 𝟐) to point 𝑵(𝟗, 𝟏𝟒). What point represents 20 miles into the trip?
Ratio: Mental Picture of Ratio
20 :80
20
80
Re
1
4
Ratio
duce
Distance
3 9
6
16
4
1 6
4 1
3
2
4
33
2
9 4.5
2
x
units
Move Units to the Right
x Coordinate or
Distance
2 14
12
112
4
1 12
4 1
3
3
2 3
5
y
units
Move Units Up
y Coordinate
9,5
2
Answer
Chapter 1 – Day 7 – Angle Measure
Objectives: SWBAT measure and classify angles.
SWBAT Identify and use congruent angles and angle bisectors.
Ray
Part of a line with a definite beginning, but no end. Must start notation with beginning of a ray
Opposite rays Two rays with a common endpoint
extending out infinitely in opposite directions Has the same properties of a line.
Angle
An angle is formed by two non-collinear rays that have a common endpoint.
Sides
The rays of an angle
Vertex
The common endpoint of an angle
Interior of an Angle Space inside the rays of an angle
Exterior of an Angle
Space outside the rays of an angle
Degrees
The unit of measurement for an angle
Written by
AB
3
Written by
QPR P
RPQ
5. Why are ∠4 and ∠𝑈 not necessarily the same angle?
Type of Angles.
Right Angle
An angle that measures 90 degrees Right angles will also get a special 90 degree box
Acute Angle
An angle that measures between 0 and 90 degrees
Obtuse Angle
An angle that measures between 90 and 180 degrees
Straight Angle
An angle that measures 180 degrees
U
&XW XU
XYU
1
U could be a couple different angles
Examples
1. Classify the following angles using a protractor and find the number of degrees.
PJM KJL NJK PJK
Right Angle Acute Angle Obtuse Angle Straight Angle
Everybody look at the clock (wait for kids to find the clock….. this might take a while). Bobby was bored, and so he decided to see what kind of angles are formed by the two arms of a clock. He looked 6:00 PM, 9:00 PM, 11:29 PM, and 4:30 PM.
However, because he was day dreaming and not paying attention, he could not remember what the differences between a straight, right, acute, and obtuse angles
(Karma). Please help out Bobby so he doesn’t look like a bum.
6:00 PM 9:00 PM 7:10 PM 4:30 PM Straight Angle Right Angle Obtuse Angle Acute Angle
PN
M
L
K
J
90 71 141 180
Chapter 1 – Day 8 – Angle Measures
Objectives: SWBAT identify and use special pairs of angles.
SWBAT identify perpendicular lines.
Congruent Angles
Angles that have the same measure, or same number of degrees.
These congruent angles can be labeled using arcs
Congruence
Equal Measure
When do I write it with a ≅
Talking about an angle in general
When do I write it as =
When you include an angle measure
Or using a number
You cannot assume congruency – you must have information that specifically tells you that the angles are congruent.
Are the following angles congruent? If they are state why, write it in both notations.
1. 2. 3.
55°
55°W
X
Y
Z
Written by
WXY YXZ
Written by
m WXY m YXZ
3 4
No
m m
Yes
ABC DEF
m ABC m DEF
Yes
W Y
m W m Y
Angle Addition Postulate:
Examples
4. If 𝒎 < 𝑬𝑭𝑯 = 𝟑𝟓 f and 𝒎 < 𝑯𝑭𝑮 = 𝟒𝟎, find the 𝒎 < 𝑬𝑭𝑮.
5. If 𝒎 < 𝟏 = 𝟐𝟐 and 𝒎 < 𝑿𝒀𝒁 = 𝟖𝟔, find the 𝒎 < 𝟐.
6. If W is in the interior of XYZ, and mXYZ =75 and mWYZ =35 , find mXYW.
Draw a Diagram. Interior means inside.
A
B
C
D
35 40
75
m EFH m HFG m EFG
m EFG
m EFG
1 2
22 2 86
22 22
2 64
m m m XYZ
m
m
m ABC m CAD m BAD
X
YZ
X
YZ
W
75 35
40
m XYZ m XYW m WYZ
m XYW
m XYW
Angle Bisector
A ray that cuts an angle into two congruent angles
7. In the Figure, BDbisects CBE . Find “x” and CBD .
Since BDbisects CBE , it cuts the two angles in two equal pieces.
So CBD DBE , and we can set them equal to each other.
Since the angles are congruent, then they have the same measurement,
so CBD is also 56 degrees
8. In the Figure, LK bisects JLM . Find JLK .
Since LK bisects JLM , it cuts the two angles in two equal pieces.
So JLK KLM , and we can set them equal to each other.
56 4
14
CBD DBE
m CBD m DBE
x
x
H
JK
L
M
N
4 15x 6 5x
4 15 6 5
15 2 5
20 2
10
JLK KLM
m JLK m KLM
x x
x
x
x
H
JK
L
M
N
A
B
C
D
E
A
B
C
D
E
56
4x
9. Find the following.
2
4 12
m ZAB x
m BAM x
m ZAB ____________
2
2
4 12
4 12 0
6 2
6 2
6
ZAB BAM
m ZAB m BAM
x x
x x
x x
x x
x only
2
26
36
m ZAB x
m ZAB
m ZAB
Chapter 1 – Day 9 – Angle Relationships – Part 1
Objectives: SWBAT identify and use special pairs of angles.
SWBAT identify perpendicular lines.
Adjacent Angles Angles that share a common ray.
Linear Pair
Adjacent angles that form a straight angle
Supplementary Angle
Angles that add up to 180 degrees.
Supplementary Adjacent Supplementary Nonadjacent AKA Linear Pair
A linear pair and supplementary angles will ALWAYS make a straight line. That
is a good way to spot a straight angle / linear pair/ supplementary angles.
Complementary Angles
Angles that add up to 90 degrees.
Complementary Adjacent Complementary Nonadjacent
Complementary Angles can be adjacent or don’t have to be adjacent.
Perpendicular Lines
Lines that intersect forming right angles
Vertical Angles
Two nonadjacent angles formed by two intersecting lines. The opposite angles formed by two intersecting lines.
Can Be Assumed
Cannot Be Assumed
Coplanar Points Perpendicular Lines
Collinear Points Complementary Angles
Betweenness of Points Congruent Angles
Intersection Points Congruent Segments
Interior / Exterior of Angles
Straight Lines (Linear pairs)
Vertical Angles
1 & 3
4 & 2
are opposite angles
are opposite angles
Written with
p m
Examples:
1. Use the diagram on the right.
a. Are 3 and 5 adjacent angles? No because they don’t share a side.
b. Are 1 and 2 adjacent angles? Yes, because they share a ray.
c. Are 1 and 2 a linear pair? No, they don’t make a straight angle.
d. Are 3 and 4 a linear pair? Yes, they are adjacent, and form a straight angle.
e. Are 2 and 4 vertical angles? No, the ray divides the angle opposite to <4
f. Are 3 and 5 vertical angles? Yes
g. If m3 = 45 then m4=________. <3 & <4 are a linear pair
h. If m5 = 53 then m3=________. <3 and <5 are vertical angles
2. Use the diagram to the right.
a. Name two pairs of complementary angles
b. What kind of angles are <RWS and <TWS?
c. What angle is supplementary <TWU?
d. Are <RWV and <VWU a linear pair? Explain why or why not.
No because they are not supplementary
3 4 180
45 4 180
135 4
m m
m
m
5
1 2
3
4
3 5
53 5
m m
m
RWQ& QWV , VEU & UWT
supplementary
UWS
Examples: Solve for the following variables.
3. 4. 5.
6. Solve for x and y. Then find the angle measures.
Notice the vertical angles!
x = _________ y = __________
mAED = _________ mAEC = _________
mCEB = _________ mDEB = _________
7. Solve for x given that a b .
Since the lines are perpendicular
Then they form right angles
13 10 16 20
10 3 20
30 3
10
y y
y
y
y
3 5 15
2 5 15
2 10
5
x x
x
x
x
6 10
6 5 10
30 10
40
m AEC m DEB
x
13 10
13 10 10
130 10
140
m AED m CEB
y
6 10( )x
13 10y
2 30( )x
16 20y
A
E
C B
D
5 25
5 25
5 5
5
Vertical Angles
x
x
x
4 136 180
4 44
11
Linear Pair
y
y
y
8 101 2 7
6 108
18
Vertical Angles
y y
y
y
2 7 3 180
2 18 7 3 180
36 7 3 180
43 3 180
3 137
137
3
Linear Pair
y x
x
x
x
x
x
2 90
45
x
x
3 90
30
y
y
Chapter 1 – Day 10 – Angle Relationships – Part 2
Objectives: SWBAT identify and use special pairs of angles.
SWBAT identify perpendicular lines.
1. Given that A and B are complementary with mA = 3x + 5 and mB = 7x + 15. Solve for x and find the measures of A and B. 2. Given that E is supp. to F . If mE = 15x + 16 and mF = 4x + 12, solve for x
and find the measures of E and F
3. A and B are supplementary. A is 127° more than B . Find the measure of each
angle.
4. The supplement of an angle is 4 times the measure of the complement of it. Find the
complement of the angle.
3 5 7 15 90
10 20 90
10 70
7
x x
x
x
x
3 5
3 7 5
21 5
26
m A
x
( )
7 15
7 7 15
49 15
64
m B
x
( )
15 16 4 12 180
19 28 180
19 152
8
x x
x
x
x
15 16
15 8 16
120 16
136
m F
x
( )
4 12
4 8 12
32 12
44
m E
x
( )
180m A m B 137m A m B 180
127 180
127 180
2 127 180
2 53
26 5
m A m B
m B m B
m B x
x x
x
x
x .
26 5
26 5
127
26 5 127
163 5
x .
m B .
m A m B
m A .
m A .
90
Complentary
x y
y complement
x angle
4 180
Supplementary
x y
90
180 4
Solving Systems
Get the same var iable
in each equation
isolated
x y
x y
90 180 4
3 90
30
Set equal and
solve
y y
y
y
4. The measure of the supplement of an angle is 30° less than 5 times the measure of the complement it. Find the supplement of the angle.
3. Given the diagram to the right, answer the following questions.
a) Can angle DBE have a complement? Why?
No, It equals 90 degrees so we can’t add another angle and Have it equal 90 (0 degrees is not an angle)
b) Are there any vertical angles present in this diagram? No, there are no vertical angles because two lines don’t
Intersect and continue past the intersection point.
c) Can there be any non-adjacent complementary angles in the diagram? No, only adjacent angles in this diagram.
d) Even though there are no numbers, why can you assume there is at least one
linear pair?
Because you can always assume a line is straight and make 180 degrees
90
Complentary
x y
y complement
x angle
5 30x y
90
5 30
Solving Systems
Get the same var iable
in each equation
isolated
x y
x y
90 5 30
6 60
10
Set equal and
solve
y y
y
y
90
90 10
80
80 180
100
x y
x
x
Supplement
x
x
Chapter 1 – Day 11 – Intro to Coordinate Geometry
Objectives: SWBAT find the perimeter and area of polygons
Perimeter
Distance around a shape or the sum of the sides
Circumference Distance around a circle
Area Space within a shape
Shape
Area
Diagram
Triangle
Square
Rectangle
Shape
Area Circumference
Diagram
Circle
2
2
Area side
A s
1
2
1
2
Area height
h
se
A
ba
b
Area heightbase
bA h
2
2
C radius
C r
2A radius
A r
Find the Area and Circumference of each figure:
1. 2.
3.
4. Find the Area of the following figure.
5m
8m
7m
2
2
Triangle
1
2
18 7
2
156
2
28
A b h
A m m
A m
A m
2
Rectangle
8 5
40
A b h
A m m
A m
2 2
2
Area Total = Rectangle + Triangle
40 28
68
TA A A
A m m
A m
5ft
15ft
13in
15m
9m
12m
2
Rectangle
15 5
75
A b h
A ft ft
A ft
2
2
2
Square
13
169
A s
A in
A in
2
Triangle
1
2
19 12
2
1108
2
54
A b h
A m m
A m
A m
2 2
2 15 2 5
30 10
40
P w
P
P
P ft
4
4 13
52
P s
P
P in
Perimeter side side side
P c b d
Examples: Graph each figure with the given vertices and identify the figure. Then find the perimeter and area of the figure.
5. A 3,2 B 1,2 C 1,-4 D 3,-4
6. A 0,0 B 3,-2 C 8,0
Need to do the distance formula to find the length of the other two sides
2
Rectangle
7 2
14
A b h
A
A units
2 2
2 2 2 7
4 14
18
P w
P
P
P units
2
Triangle
1
2
18 2
2
8
A b h
A
A units
8 13 29
8 13 29
P
No Like Terms
P units
2 2
2 1 2 1
2 2
2 2
3 0 2 0
3 2
9 4
13
d x x y y
d
d
d
d
2 2
2 1 2 1
22
2 2
8 3 0 2
5 2
25 4
29
d x x y y
d
d
d
d
7. Find the area and circumference of the circle with Center at (0,0) and goes through the point (5,0).
2
2 5
10
C r
C
C units
2
2
2
5
25
A r
A
A units