Question

question 9 of 10
is \\( \triangle x y z \cong \triangle a b c \\) ? if so, name the postulate that applies.

given:
\\( \angle y \cong \angle b \\)
\\( \overline{x y} \cong \overline{a b} \\)
\\( \overline{y z} \cong \overline{b c} \\)

a. might not be congruent
b. congruent - sas
c. congruent - asa
d. congruent - sss

Explanation:

Step1: Recall congruent triangle postulates

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: Check the given information

We are given that \(\overline{XY}\cong\overline{AB}\), \(\angle Y\cong\angle B\), and \(\overline{YZ}\cong\overline{BC}\). Here, \(\angle Y\) is the included angle between \(\overline{XY}\) and \(\overline{YZ}\) in \(\triangle XYZ\), and \(\angle B\) is the included angle between \(\overline{AB}\) and \(\overline{BC}\) in \(\triangle ABC\).

Answer:

B. Congruent - SAS