Question

The SAS (side-angle-side) relationship is a way to show that triangles are congruent. Sets of triangle parts are listed. Which set gives parts that allow triangle ABC to be proven congruent to triangle XYZ by SAS?

A. OA = 2X; ZB = ZY; AB = XY

B. ZA = LX; LBS LY; ZCELZ

C. ZAS ZX; AB = XY; AC = XZ

D. ZA ZX; BC YZ; AC XZ

Answer 1

To prove that triangle ABC is congruent to triangle XYZ using the SAS relationship, we need to have two pairs of corresponding sides that are congruent and the included angles between these sides to be congruent. The set of triangle parts in option C, ZAS ZX; AB = XY; AC = XZ, satisfies these conditions.

Step-by-step explanation:

The SAS (side-angle-side) relationship is a way to show that triangles are congruent. To prove that triangle ABC is congruent to triangle XYZ using the SAS relationship, we need to have two pairs of corresponding sides that are congruent and the included angles between these sides to be congruent. Looking at the sets of triangle parts, the set in option C matches these criteria. The set ZAS ZX represents the corresponding sides of the triangles that are congruent, and the sides AB = XY and AC = XZ ensure that the included angles between these sides are congruent.