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