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Angle Packet Name__________________________________ Per.: ___

Definition: An angle is formed by two rays

that share a common endpoint.

1. The point that the two rays intersect is called the ________________________. 2. The two rays are called the ______________________ of the angle. 3. When naming angles, it is typical to use one or three letters. Sometimes one cannot use

one letter. When using three letters, the ____________________ must be the letter in

the middle. Other times one uses numbers to name the angles as below.

4. Name an angle using one letter. _________

5. Name three different angles. _________, __________, _________

6. IRC can also be named in what two other ways? , An angle breaks up a plane into three regions:

the exterior of the angle the interior of the angle points on the angle.

7. Name the points on the interior of FAB , , ,

8. Name the points on FAB. , , ,

•

• • M

A

X

R

I C

K •

• •

•

•

• • M

A

X

1 2

S •

M •

A • R • T •

F •

B • Y •

N •

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Find the measure of each angle and classify it right, acute, obtuse, or straight. a) VDS b) SDL c) IDS d) SDE I V L E D S

Suppose mKNL = 110 and mLNM = 25.

What would you do to find the mKNM?

Suppose mMNK = 155 and mLNM is 30. What would you do to find the mLNK?

K N

L

M

K N

L

M

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Angle Addition Postulate

For any ABC, if D is in the interior of ABC, then mABD + mDBC = mABC. Draw a diagram below to show this.

Angle Bisector A _______ that divides an angle into ____________ angles of equal ________________ is called the __________________ _________________.

1. Find m1 if mCUB = 78. 2. Find m2 if mWHI = 160.

3. mSOX = 160

m1 = x + 14

m2 = 3x – 10

Find m2

4. mBEA = 71. Find mREA.

S

O

W

1 2 X

B U

S C

1

48

W

T

H

E

I

104

2 42

A

B

E R

(5x + 8)

2x

4

5. mWOV = 12x. Find mLOV.

6. mFIE = 3x, mRIE = 42, mFIR = 5x

Find mFIR.

8. US bisects BUL, mBUS = 2x + 10,

and mSUL = 3x – 18.

Find mBUL.

9. mTRI = 3x – 5, mIRB = x + 27,

and mTRB = 86.

Does RI bisect TRB?

W

O

L

V

76 (5x + 1)

B

U

S

L

T

R

B

I

F E

I

R

5

10. Find the measure of each angle.

a. mNEO = _______ b. mDES = _______

c. mDEO = _______ d. mSEO = _______

Complementary and Supplementary Angles

Two angles whose measures add up to 180⁰ are called _____________________________ __________.

They can also be called a __________________ __________ if together they form a straight angle.

Two angles whose measures add up to 90⁰ are _______________________________ ___________.

In the diagram above, ________ and ________ are ______________________________ ___________.

In the other diagram above, ________ and ________ are ____________________________ _________.

Supplementary and Complementary Angles Find the measures of angles 1 through 13. Mark them in your diagram.

C

B

A D

50° 40°

R T

S E C

D

N

O 27

18

57 1

71 2

3

4 5

104

6

14) Find mDBC.

15) Find mDBC.

16) 1 and 2 are complementary. m1 = 2x + 7 and m2 = 4x – 19. Find the measure of each

angle.

17) 3 and 4 are supplementary. m3 = 5x + 22 and m4 = 7x + 2. Find the measure of each

angle.

18) Use the diagram on the right to name:

a) two complementary angles

b) a linear pair

c) two adjacent angles

75 62

8 7

6

B C A

x

D

8x

(4x – 20)

x

A B

C

D

12 13

122 42

11

10

9

A

D

C

B

E

F

G • •

•

•

•

•

•

7

Name_________________________________________ Date________ Hour____

3.6 – Vertical Angles

Geometry G

Vertical Angles:

THEOREM:

Examples:

1) Find x, y, and z

x

51 Y

z

2) Given: m4 = (2x + 5)

m5 = (x +30)

Find: m6

3) Identify each pair of angles as adjacent, vertical, complementary, supplementary, and/or linear pair.

a) 1 and 2

b) 3 and 4

c) 5 and 4

1 2

3 4

4 5 6

1

2

3 4 5

8

d) 3 and 5

4) Find x and y if CBD is congruent to FDG.

5) Find each of the following:

a) x

b) mLAT

c) mTAO

d) mPAO

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Vocabulary Words:

Complementary Angles Supplementary Angles Right Angles Angle Bisector Linear Pair Vertical Angles

Adjacent Angles.

ST bisects RSW

1. In the pictures above, FOH and GOH are called _____________________________.

2. FOH and GOH are also called ____________________________________________.

3. Further, FOH and GOH are _____________________________________________.

4. In the pictures above, ACB and DCE are called ______________________________.

5. In the pictures above, JPK and KPL are called ______________________________.

6. JPK and KPL are also called ___________________________________.

7. Name the vertical angle ACD to ___________________________________.

8. What do you know about RST and TSW? ___________________________________

9. What do you call LPM? ___________________________________

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In the figure, GA and GD, and GB and GE are opposite rays. 10] Which angle forms a linear pair with DGC ? ________

11] Do BGC and EGD form a linear pair? ________

12] Name two angles that are adjacent to CGD . ________ ________

13] Name two angles that form a linear pair with BGD . ________ ________

14] Name three angles adjacent to AGB . ________ ________ ________

15] Do CGE and CGB form a linear pair? ________

16] Name the vertical angle to EGD . _______________

17] Name another pair of vertical angles. ____________ and _______________

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Name: Name: 1] a linear pair 2] a pair of supplementary angles 3] a pair of complementary angles 4] a pair of adjacent angles 5] a pair of vertical angles 6] two right angles Write each pair of angles that you named above into the proper column of the table below.

Angle Relationships

Equals Equals 180 Equals 90

A

B

C

E

F G

D

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Determine the relationship in the diagram.

Are the angles complementary or is it a right angle? The angles add to 90.

Are the angles supplementary or are they a linear pair? The angles add to 180.

Do you have an angle bisector? The two angles are congruent. Do you have vertical angles? The two angles are congruent.

Write the equation and then solve the equation. 1. 2. Equation: _______________________ Equation: _______________________ x = ______ x = ______ 3. 4. Equation: _______________________ Equation: _______________________ x = ______ x = ______

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5. 6. Equation: _______________________ Equation: _______________________ x = ______ x = ______ 7. 8. Equation: _______________________ Equation: _______________________ x = ______ x = ______

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________m ACB = _________m ABC =

3.7 – Perpendicularity Name____________________________

Geometry G Date___________________ Hour_____ NOTES Perpendicularity, _____________________, and __________ measurements go together. Definition: If lines, rays or segments form right angles, then they are perpendicular( ). What would be the converse of the definition? Examples:

a ⊥ b DE EF⊥

What conclusions would I be able to make if given the following: AB BC⊥ 1) 2)

D

E

F

a

b

A

B C

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Example 1: True or False?

1. PRN is acute. 2. 48

3. m5 + m6 = 90

4. QR PR⊥

5. 7 is obtuse

Example 2: Find x. Example 3: Find mDBC.

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Geometry G Name____________________________ Section 2.5. Worksheet 3 Warm – Up: 1. 2.

________=FOHm ST bisects RSW , = 27RSTm

_________=TSWm _________=WSRm

3. 4.

_________=JPKm 70m CBF = & BD bisects .CBF

_________=JPLm ________m CBD = ________=ABCm

5. AB ⊥ CD ________=DCEm

CE bisects DCB ________=ACDm

________=DCBm

6. ________=DBCm

________=CBEm

BC bisects DBE ________m DBE =

18

7. _________=ABEm

_________=DBCm

8. BD bisects ABC and = 32ABDm

_________=DBCm

_________m ABC =

9. ______1=m

______2 =m ______3 =m

______4 =m

5 ______m =

______6 =m

______7 =m

10. AB ⊥ CD ________1=m

HE bisects CHB

32m BHG = ________2 =m

________3 =m

________4 =m

________5 =m

________6 =m

________7 =m

Given l⊥ p

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Determine the relationship in the diagram.

Are the angles complementary or is it a right angle? The angles add to 90.

Are the angles supplementary or are they a linear pair? The angles add to 180.

Do you have a angle bisector? The two angles are congruent. Do you have vertical angles? The two angles are congruent.

Write the equation and then solve the equation. 1. 2. Equation: _______________________ Equation: _______________________ x = ______ x = ______ 3. 4. Equation: _______________________ Equation: _______________________ x = ______ x = ______

_______=ABCm _______=ABCm

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Geometry G Name____________________________ Section 2.5. Worksheet 6 5. 6. Equation: _______________________ Equation: _______________________ x = ______ x = ______

_______=ABCm _______=ABCm

Note: Picture is not drawn to scale. 7. BD bisects ABC 8.

Equation: _______________________ Equation: _______________________ x = ______ x = ______

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_______=ABCm _______m EBD =

22

9. Equation: _______________________ x = ________ ________=AFDm

________=AFBm ________=CFDm

10. 11. Equation:_________________________ Equation:_________________________

x = ________ x = ________

________=ABCm ________=PQRm

________=ABEm ________=RQTm

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Geometry G Name____________________________ Section 2.5. Worksheet 7 Determine the relationship in the diagram.

Are the angles complementary or is it a right angle? The angles add to 90.

Are the angles supplementary or are they a linear pair? The angles add to 180.

Do you have an angle bisector? The two angles are congruent. Do you have vertical angles? The two angles are congruent.

Write the equation and then solve the equation. 1. 2. Equation: _______________________ Equation: _______________________ x = ______ x = ______ 3. 4. Equation: _______________________ Equation: _______________________ x = ______ x = ______

_______=ABCm _______=ABCm

8x (7x + 10) (6x + 12)

(16x + 4) (18x + 4)

18x (16x + 4)

(7x - 12)

(5x + 18)

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