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Ben uses a compass and a straightedge to construct ∠DEF ≅ ∠ABC, as shown below:

Which statement best explains why Ben uses the width BI to create the arc JK from point E?

A ∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.
B BI = JK when ∠DEF ≅ ∠ABC.
C BI = EJ when ∠DEF ≅ ∠ABC.
D ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

Ben Uses A Compass And A Straightedge To Construct DEF ABC As Shown Below Which Statement Best Explains Why Ben Uses The Width BI To Create The Arc JK From Poin class=

Answer :

Answer: Choice D

∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

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Explanation:

Effectively what Ben is doing is ensuring that

  • BH = EJ
  • BI = EK
  • HI = JK

are the three congruent corresponding sides. This is by construction. After those constructions, he would use SSS to prove the triangles congruent. Lastly, he can then say angle DEF is congruent to angle ABC due to CPCTC.

CPCTC = corresponding parts of congruent triangles are congruent.

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