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.constructing ΔABC so that AB ≅ XY, BC ≅ YZ, and CA ≅ ZXconstructing ΔABC so that AB ≅ XY, BC ≅ YZ, and ∠C ≅ ∠Zconstructing ΔABC so that AB ≅ XY, CA ≅ ZX, and ∠A ≅ ∠Xconstructing ΔABC so that CA ≅ ZX, ∠B ≅ ∠Y, and ∠C ≅ ∠Zconstructing ΔABC so that ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z
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 guarantees congruence by SAS: the two matching sides meet at the matching angle A and X. D guarantees congruence by AAS: the two matching angles determine the third angle as well, and a corresponding side matches. B gives SSA, which can describe different triangles, and E gives only AAA, which guarantees similarity but not necessarily equal size.
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