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Chapter 3: Q2 (page 80)

If c鈭�d, name all angels that must be congruent to 鈭�1.

Short Answer

Expert verified

Angles congruent to鈭�1is鈭�6,鈭�9,and鈭�14.

Step by step solution

01

Step 1. Observations from figure

a is transversal to parallel linescandd

02

Step 2. Find corresponding angles

Corresponding angle to 鈭�1is 鈭�9

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

Thus,鈭�1鈮�鈭�9

03

Step 3. Find vertically opposite angles

Vertically opposite angle to 鈭�1is鈭�6

Vertically opposite angle to 鈭�9is 鈭�14

Theorem 2-3: Vertically opposite angles are congruent, so 鈭�1鈮�鈭�6and鈭�9鈮�鈭�14.

04

Step 4. Use transitive property

If a=band b=cthen a=c

Substitute 鈭�1for a,鈭�6 for b, and 鈭�14for c

Since, 鈭�1鈮�鈭�6and 鈭�6鈮�鈭�14implies鈭�1鈮�鈭�14

Thus, angles congruent to 鈭�1is鈭�6,鈭�9,and鈭�14

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