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2.7 Prove Angle Pair RelationshipsPowerPoint Presentation

2.7 Prove Angle Pair Relationships

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2.7 Prove Angle Pair Relationships

Objectives

- Write proofs involving supplementary and complementary angles
- Write proofs involving congruent and right angles

Theorems & Postulates

- Theorem 2.3 (Right Angles Theorem) All right angles are congruent.
- Theorem 2.4 ( Supplement Theorem) If 2 angles are supplementary to the same angle (or congruent angles), then they are congruent.
- Theorem 2.5 ( Complement Theorem )If 2 angles are complementary to the same angle (or congruent angles), then they are congruent.

Theorems & Postulates

- Postulate 12 ( Linear Pair Postulate)If 2 angles form a linear pair, then they are supplementary
- Theorem 2.6 (Vertical Angles Theorem)
Vertical angles are congruent.

In the figure, form a linear pair, and Prove that are congruent.

and

and

Given: form a linear pair.

Prove:

Example 1:Proof: Prove that are congruent.

Statements Reasons

1.

1. Given

2.

2. Linear pairs are supplementary.

3.

3. Definition of supplementary angles

4.

4. Subtraction Property

5.

5. Substitution

6.

6. Definition of congruent angles

Example 1: 1 & 4 linear pair;

Your Turn: Prove that are congruent.

In the figure, NYR and RYA form a linear pair,AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that RYN and AXYare congruent.

Proof: Prove that are congruent.

Statements Reasons

1.

1. Given

linear pairs.

2.

2.If two s form a linear pair, then they are suppl. s.

3.

3.Given

4.

4.

Your Turn:If Prove that are congruent.1 and 2are vertical angles and m1 andm2 find m1 and m2.

1

2

Vertical Angles Theorem

m1

m2

Definition of congruent angles

Example 2:Substitution

Add 2d to each side.

Add 32 to each side.

Divide each side by 3.

Example Prove that are congruent.2:

Answer: m1 = 37 and m2 = 37

If and are vertical angles and Prove that are congruent.

and

find and

Your Turn:Answer: mA= 52; mZ= 52

form a linear pair and Prove that are congruent.

If

and

find

Example 3:Supplement Theorem

Subtraction Property

Answer: 14

Assignment Prove that are congruent.

- Geometry: Pg. 127 – 131
#3 - 29, 38, 42, 46

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