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Assume that aband cd, name all angels congruent to 2.

Short Answer

Expert verified

Angles congruent to 2is4,5,7,10,12,13,and15.

Step by step solution

01

Step 1. Observations from figure

  • ais transversal to parallel linescandd
  • bis transversal to parallel lines cand d
  • cis transversal to parallel linesaandb
  • dis transversal to parallel linesaandb
02

Step 2. Find corresponding angles

Corresponding angle to 2is 4and 10

Corresponding angle to 4is12

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

Thus,24,210,and412

03

Step 3. Find vertically opposite angles

Vertically opposite angle to 2is5

Vertically opposite angle to 4is 7

Vertically opposite angle to 10is13

Vertically opposite angle to 12is 15

Theorem 2-3: Vertically opposite angles are congruent, so 25,47,1013,and1215

04

Step 4. Use transitive property

If a=band b=cthen a=c

24,41221224,4727210,1013213212,1215215

Thus, angles congruent to 2is4,5,7,10,12,13,and15.

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