MATH325: Proof Correction


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Find and correct any errors in the following proof:

Theorem: Let triangles ABC and A'B'C' be two triangles such that angle BAC is congruent to angle B'A'C' and:

|A'B'|/|AB| = |A'C'|/|AC|.

Prove that triangles ABC and A'B'C' are similar.

Proof: We're told that |A'B'|/|AB| = |A'C'|/|AC|. Therefore, by Theorem 1.7.3, segment B'C' is parallel to segment BC.

Because they are alternate interior angles, angles A'B'C' and ABC are congruent.
Because they are alternate interior angles, angles A'C'B' and ACB are congruent.

We're told that angles B'A'C' and BAC are congruent, so by the definition of similar triangles, triangles A'B'C' and ABC are congruent.//