Chapter 2.8

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Chapter 2.8. Proving Angle Relationships. Concept. Concept. Use the Angle Addition Postulate. Prove that the m&lt;1 = 89 , if m&lt;2 = 56 and m&lt;JKL = 145. J. K. 2. 1. L. Example 1. Prove that the m  1 = 104 if m  2 = 58 and m  JKL = 162. Concept. Concept. Example 2.

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### Chapter 2.8

Proving Angle Relationships

Prove that the m<1 = 89, if m<2 = 56 and m<JKL = 145.

J

K

2

1

L

Example 1

Prove that the m1 = 104 if m2 = 58 and mJKL = 162.

Example 2

QUILTINGThe diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.

A. 20

B. 30

C. 40

D. 50

Given:

Prove:

Example 3

Proofs Using Congruent Comp. or Suppl. Theorems

Proof:

Statements Reasons

1. m3 + m1 = 180;1 and 4 form a linear pair.

1. Given

2. 1 and 4 are supplementary.

2. Linear pairs are supplementary.

3. 3 and 1 are supplementary.

3. Definition of supplementary angles

4. 3  4

4. s suppl. to same  are .

Example 3

Proofs Using Congruent Comp. or Suppl. Theorems

Example 3

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 NYR and AXY are congruent.

Statements Reasons

1. NYR and RYA, AXY and AXZ form linear pairs.

1. Given

2. NYR and RYA are supplementary. AXY and AXZ are supplementary.

2. If two s form a linear pair, then theyaresuppl.s.

3. Given

3. RYA  AXZ

?

4. ____________

4.NYR  AXY

Example 3

Which choice correctly completes the proof?

Proof:

Proof:

Statements Reasons

Example 4

Use Vertical Angles

If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.

1. 1 and 2are vertical s.

1. Given

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• Pg. 157 #22 - 26