Question

question 8 of 10
is △xyz ≅ △abc? if so, name the postulate that applies.
given:
∠y ≅ ∠b
xy ≅ ab
yz ≅ bc
a. congruent - asa
b. might not be congruent
c. congruent - sas
d. congruent - sss

Explanation:

Step1: Recall SAS Postulate

The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze Given Information

We are given that $\angle Y\cong\angle B$, $\overline{XY}\cong\overline{AB}$, and $\overline{YZ}\cong\overline{BC}$. In $\triangle XYZ$, the angle $\angle Y$ is between sides $\overline{XY}$ and $\overline{YZ}$. In $\triangle ABC$, the angle $\angle B$ is between sides $\overline{AB}$ and $\overline{BC}$. So we have two sides and the included angle of $\triangle XYZ$ congruent to two sides and the included angle of $\triangle ABC$. This satisfies the SAS postulate.

Answer:

C. Congruent - SAS