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2.7 Prove Angle Pair Relationships PowerPoint PPT Presentation


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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.

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2.7 Prove Angle Pair Relationships

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2 7 prove angle pair relationships

2.7 Prove Angle Pair Relationships


Objectives

Objectives

  • Write proofs involving supplementary and complementary angles

  • Write proofs involving congruent and right angles


Theorems postulates

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 postulates1

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.


Example 1

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

and

and

Given: form a linear pair.

Prove:

Example 1:


Example 11

Proof:

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

Your Turn:

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.


Your turn1

Proof:

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:


Example 2

If 1 and 2are vertical angles and m1 andm2 find m1 and m2.

1

2

Vertical Angles Theorem

m1

m2

Definition of congruent angles

Example 2:

Substitution

Add 2d to each side.

Add 32 to each side.

Divide each side by 3.


Example 21

Example 2:

Answer: m1 = 37 and m2 = 37


Your turn2

If and are vertical angles and

and

find and

Your Turn:

Answer: mA= 52; mZ= 52


Example 3

form a linear pair and

If

and

find

Example 3:

Supplement Theorem

Subtraction Property

Answer: 14


Your turn3

If

are complementary angles and .

and

find

Your Turn:

Answer: 28


Assignment

Assignment

  • Geometry: Pg. 127 – 131

    #3 - 29, 38, 42, 46


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