Proving Angle Pair Relationships

2.6 Intro - Special Angles / Proof Reasons

​Intro to Angle Proofs

First, you will review some of the angle relationships that you learned in Unit 1....

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​Then, you will have a chance to practice using these definitions, postulates, and theorems like you will soon do when completing angle proofs!

​Angle Addition Postulate

Multiple Choice

Solve

• 50°
• 58°
• 115°
• 226°

Multiple Choice

What does the Angle Addition Postulate say about this picture?

• m<ADC = m<ADB + m<BDC

• m<ABC = m<ADB + m<BDC

• m<BDC = m<ADB

• m<ADC = 2m<ADB

Recall what we know about angles that form a linear pair...

Multiple Choice

Which of the following is a linear pair?

Multiple Choice

Find the measure of angle b.

• $$106\degree$$

• $$28\degree$$

• $$96\degree$$

• $$118\degree$$

Multiple Choice

Linear pair angles are adjacent

• sometimes

• always

• never

Multiple Choice

Supplementary angles are adjacent.

• sometimes

• always

• never

​We also know a special relationship

for 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

Vertical angles are always

• acute
• total 180 degrees
• congruent (equal measures)
• adjacent angles

Multiple Choice

If <A and <B form a linear pair, then <A and <B are supplementary.

• Congruent Supplements Theorem

• Linear Pair Postulate

• Definition of Supplementary Angles

• Definition of a Right Angle

Multiple Choice

Which angles are vertical angles?

• $$\angle8\ \ and\ \angle7$$

• $$\angle8\ and\ \angle6$$

• $$\angle8\ and\ \angle5$$

Multiple Choice

Angles 4 and 1 are what angle pair?

• Complementary
• Linear Pair
• Acute
• Vertical

Multiple Select

Name the relationship between the angles.

SELECT ALL THAT APPLY.

• Complementary

• Linear Pair

• Vertical

• Supplementary

• Adjacent

Now, you will be answering questions based on the properties, definitions, postulates, and theorems you have learned so far!

These will help us get ready for angle proofs next week and will help us review segment proofs that we have already done!​

Multiple Choice

If ∠A and ∠B are complementary,
then m∠A + m∠B = 90°.

• Definition of Supplementary Angles
• Angle Addition Postulate
• Definition of Right Angle
• Definition of Complementary Angles

Multiple Choice

Which postulate or definition states that
m∠ADB + m∠BDC = m∠ADC?

• Segment Addition Postulate
• Angle Addition Postulate
• Definition of Angle Bisector
• Definition of Congruent Angles

Multiple Choice

If ∠1 and ∠2 are supplementary,

then m∠1 + m∠2 = 180°.

• Definition of Supplementary Angles

• Angle Addition Postulate

• Vertical Angles Theorem

• Linear Pair Postulate

Multiple Choice

If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.

• Addition Property of Equality

• Symmetric Property of Congruence

• Reflexive Property of Congruence

• Transitive Property of Conguence

Multiple Choice

If ∠CAT is a right angle, then m∠CAT = 90°.

• Definition of Right Angle
• Definition of Congruent Angles
• Angle Addition Postulate
• Segment Addition Postulate

Multiple Choice

If ∠BAT and ∠MAN are vertical angles,
then ∠BAT ≅ ∠MAN.

• Vertical Angles Theorem
• Definition of Congruent Angles
• Angle Addition Postulate

Multiple Choice

If m∠DOG = m∠CAT, then ∠DOG ≅ ∠CAT.

• Definition of Congruent Angles
• Definition of Congruent Segments
• Angle Addition Postulate
• Vertical Angles Theorem

Multiple Choice

If ray BD bisects ∠ABC, then ∠ABD ≅ ∠CBD.

• Definition of Congruent Angles

• Definition of Angle Bisector

• Angle Addition Postulate

• Definition of Right Angle

Multiple Choice

What is the justification (reason)?

• reflexive property

• definition of segment bisector

• definition of a midpoint

• substitution property

Multiple Choice

Perpendicular lines intersect to form...

• 1 right angle

• 2 right angles

• 3 right angles

• 4 right angles