Exploring Angle Pairs in Geometry

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Lesson 1-5:
Exploring Angle
Pairs

Objective: SW identify
special angle pairs and
use their relationships
to find angle measures.

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Congruent Angles

Angles with the same measure are congruent angles. This
means that if m∠A = m∠B, then ∠A ≅∠B. You can also
say that if ∠A ≅∠B, then m∠A = m∠B.

You can mark angles with arcs to
show that they are congruent.
If there is more than one set of
congruent angles, each set is
marked with the same number
of arcs.

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Types of
Angle pairs

• Common side and a

• Common vertex.
  
  

​

​Adjacent

Angles have a:

Multiple Select

Which are pairs of adjacent angles? Select all that apply.

• ∠1 & ∠3

• ∠2 & ∠3

• ∠1 & ∠2

Multiple Choice

True or False

Angles 1 and 2 are adjacent angles.

• True

• False

Multiple Select

Which angles are adjacent with $$\angle8$$  ?

• $$\angle1$$  

• $$\angle6$$  

• $$\angle7$$  

• $$\angle5$$  

• $$\angle9$$  

• Are opposite from each other and

• Are congruent.

​

​Vertical Angles:

Multiple Choice

Which are pairs of vertical angles?

• ∠COB & ∠COA

• ∠AOD & ∠AOC

• ∠COB & ∠AOD

• ∠BOD & ∠AOD

Multiple Choice

If m∠1 = 30°, then m∠3 =

• 30°

• 60°

• 150°

• undetermined

Multiple Choice

Which angle is vertical angle to $$\angle7$$  ?

• $$\angle1$$  

• $$\angle5$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle9$$  

Multiple Choice

Which angles are vertical angles?

• $$\angle8\ \&\ \angle7$$

• $$\angle8\ \&\ \angle6$$

• $$\angle8\ \&\ \angle5$$

Multiple Choice

Which angle is complementary to $$\angle LJM$$  ?

*Also called the complement of angle LJM.

• $$\angle MJN$$  

• $$\angle NJP$$  

• $$\angle FGE$$  

• $$\angle LJK$$  

Multiple Choice

Find the missing angle.

• 53

• 67

• 77

• 43

Multiple Choice

How are these angles related?

• Vertical

• Complementary

• Adjacent

• Supplementary

Multiple Choice

What term is used to describe a pair, or group, of angles that equal 180 degrees?

• Supplementary Angles

• Complementary Angles

• Vertical Angles

• Congruent Angles

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Making Conclusions From a Diagram

Can you conclude the following information from the diagram?

1. ∠1 ≅∠2 by the markings

2. ∠2 and ∠4 are vertical angles

3. ∠3 and ∠5 are vertical angles

4. ∠1 and ∠5 are adjacent angles

5. ∠1 and ∠2 are adjacent angles

6. ∠3 and ∠4 are adjacent supplementary angles

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Postulate 1-9

Linear Pair Postulate

If two angles form a linear pair, then they are
supplementary.

A linear pair is a pair of adjacent
angles whose noncommon sides
are opposite rays. The angles of
a linear pair form a straight
angle.

Multiple Choice

A straight angle equals...

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

Multiple Select

What kind of angles are these? (Choose all that apply)

• complementary

• supplementary

• right

• linear pair

Multiple Choice

Name a pair of angles that form a linear pair.

• Angles 1 and 2

• Angles 2 and 4

• Angles 5 and 8

• Angles 9 and 10

Multiple Choice

Find the m∠3.

• 28

• 152

• 180

• 62

Drag and Drop

Use the information given at the left to find m∠KPL and m∠JPL.

m∠KPL =​

Placeholder

and m∠JPL =​

Placeholder

Drag these tiles and drop them in the correct blank above

20

6

36

54

144

90

64

116

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Angle Bisector

An angle bisector is a
ray that divides an angle
into two congruent
angles.

Multiple Choice

Ray AC bisects ∠DAB. Find m∠CAB and ∠DAB.

• m∠CAB = 58, m∠DAB = 116

• m∠CAB = 58, m∠DAB = 58

• m∠CAB = 29, m∠DAB = 58

• m∠CAB = 29, m∠DAB = 29

Fill in the Blanks

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In the question below, ray AB is the angle bisector of
∠CAD. Solve for the missing variable.

Audio Response

In the figure at the left, ray AB is the angle bisector of ∠CAD. Solve for the missing variable.

x = _____

Open Audio Recorder

Multiple Choice

Angle GHJ measures 161⁰. Ray HK bisects ∠GHJ. Find m∠GHK and m∠KHJ.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

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