Chapter 4.4, Problem 35STP

To determine

The information needed to prove that triangle ABC is congruent to triangle XYZ.

Answer to Problem 35STP

Option F. $\overline{BC}\cong \overline{YZ}.$ is correct.

Explanation of Solution

Given:

  $\angle C\cong \angle Z\text{ and }\overline{\text{AC}}\cong \overline{XZ}.$

  

Calculation:

According to the SAS Congruence Postulate, if the 2 sides and the included angle of the first triangle are congruent to the 2 sides and the included angle of the second triangle, then the two triangles are congruent.

One pair of corresponding sides is congruent and also one pair of corresponding angles is congruent.

  

For the SAS Congruence Postulate to apply, $\overline{BC}\cong \overline{YZ}$ so that $\angle C\text{ and }\angle Z$ are a pair of included angles.

  

Hence, Option F. $\overline{BC}\cong \overline{YZ}.$ is correct.