Mathematics, 04.03.2021 20:10 silviamgarcia
Bill constructs △ABC and △DEF such that ∠A≅∠D and ∠B≅∠E. He claims that the two triangles are similar. To prove his claim, he constructs △AB'C' as a dilation of △ABC from center A such that AB' = DE.
Bill then provides the following reasoning to justify his claim.
Since ∠A≅∠D by construction, ∠B'≅∠E by the Transitive Property applied to ∠B'≅∠B (by the Corresponding Angles Theorem) and to ∠B≅∠E (by construction), and AB'¯¯¯¯¯¯≅DE¯¯¯¯¯ by construction, it follows that △AB'C' and △DEF are congruent by the AAS triangle congruence criterion. It then follows that △ABC and △DEF are similar as there is a sequence of rigid motions and dilations that carries △ABC to △DEF.
Which of the following statements BEST describes Bill's reasoning?
A. The reasoning is entirely correct as written.
B. The reasoning would be correct if AAS is changed to ASA.
C. The reasoning would be correct if Corresponding Angles Theorem is changed to Alternate Interior Angles Theorem.
D. The reasoning is not correct because the congruence of △AB'C' and △DEF has no relevance to the similarity of △ABC and △DEF.
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