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Chapter 3: Q1 (page 80)

If a∥b, name all angels that must be congruent to ∠1.

Short Answer

Expert verified

Angles congruent to∠1is∠3,∠6,and∠8.

Step by step solution

01

Step 1. Observations from figure

cis transversal to parallela linesb.

02

Step 2. Find corresponding angles

Corresponding angle to ∠1is ∠3

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent.

Thus,∠1≅∠3

03

Step 3. Find vertically opposite angles

Vertically opposite angle to ∠1is∠6

Vertically opposite angle to ∠3is ∠8

Theorem 2-3: Vertically opposite angles are congruent, so∠1≅∠6 and∠3≅∠8.

04

Step 4. Use transitive property

If a=band b=cthen a=c

Substitute ∠1for a,∠3for b, and ∠8for c

Since, ∠1≅∠3and ∠3≅∠8implies ∠1≅∠8

Thus, angles congruent to ∠1is ∠3,∠6,and∠8

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