6
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Right Triangle Similarity

Question 6 • *CR CCSS Math 2 S2 [M2960OX]

Suppose ΔXYZ is given, and you want to construct ΔABC so that the triangles are congruent. Which constructions would guarantee that ΔXYZ ≅ ΔABC? Check all that apply.

Answer
A
constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZX
B
constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and ∠C ≅ ∠Z
C
constructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠X
D
constructing ΔABC so that CA ≅ ZX, ∠B ≅ ∠Y, and ∠C ≅ ∠Z
E
constructing ΔABC so that ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z

Explanation

A guarantees congruence by SSS: all three corresponding sides match. C gives two corresponding sides and the included angle (SAS), since ∠A lies between AB and AC. D gives two corresponding angles and a corresponding side (AAS), which determines the triangle. B is SSA, which can produce different triangles, and E is AAA, which guarantees similarity but not necessarily congruence.

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