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Chapter 3: Q1 (page 80)

If a鈭�b, name all angels that must be congruent to 鈭�1.

Short Answer

Expert verified

Angles congruent to鈭�1is鈭�3,鈭�6,and鈭�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 鈭�1is 鈭�3

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

Thus,鈭�1鈮�鈭�3

03

Step 3. Find vertically opposite angles

Vertically opposite angle to 鈭�1is鈭�6

Vertically opposite angle to 鈭�3is 鈭�8

Theorem 2-3: Vertically opposite angles are congruent, so鈭�1鈮�鈭�6 and鈭�3鈮�鈭�8.

04

Step 4. Use transitive property

If a=band b=cthen a=c

Substitute 鈭�1for a,鈭�3for b, and 鈭�8for c

Since, 鈭�1鈮�鈭�3and 鈭�3鈮�鈭�8implies 鈭�1鈮�鈭�8

Thus, angles congruent to 鈭�1is 鈭�3,鈭�6,and鈭�8

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Most popular questions from this chapter

Find the values of x,yand z

State which segments (if any) are parallel. State the postulate or theorem that justifies your answer.

Name the two lines and the transversal that form each pair of angles.

and

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

and

Given: AS炉鈭�BT炉;m鈭�4=m鈭�5; SB鈫�bisects 鈭�AST

Find the measure of鈭�1
See all solutions

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