Question

What else would need to be congruent to show that ABC=AXYZ by SAS?

A. ZB=LY
B. BC = YZ
C. C= LZ
D. AC = XZ
Given:
AB XY
BC=YZ

Answer 1

To prove triangle congruence by SAS, along with the given congruent sides AB = XY and BC = YZ, the angle between those sides (angle C in triangle ABC and angle LZ in triangle XYZ) must also be congruent.

Step-by-step explanation:

The student is asking about conditions required to prove triangle congruence using SAS (Side-Angle-Side), which is a congruence postulate in geometry. Given that side AB is congruent to side XY, and side BC is congruent to side YZ, we need to prove that an angle included between those pairs of sides is also congruent.

For triangles ABC and XYZ to be congruent by SAS, along with the two pairs of sides that are given as congruent (AB = XY and BC = YZ), the angle between those sides in each triangle needs to be congruent. Therefore, the correct answer is C. C = LZ, which means that angle C in triangle ABC must be congruent to angle LZ in triangle XYZ.