Question

What additional information would be necessary to prove that the two triangles, rxby and rzay, are congruent?

1) Side-Side-Side (SSS) congruence theorem
2) Side-Angle-Side (SAS) congruence theorem
3) Angle-Side-Angle (ASA) congruence theorem
4) Angle-Angle-Side (AAS) congruence theorem

Answer 1

The additional information needed to prove the congruence of triangles rxby and rzay is the Angle-Side-Angle (ASA) congruence theorem, which requires specific angle and side relationships to be satisfied.

Step-by-step explanation:

The additional information that would be necessary to prove that the two triangles, rxby and rzay, are congruent can be determined by the congruence theorem.

In this case, the correct theorem to be used is the Angle-Side-Angle (ASA) congruence theorem.

To prove congruence using ASA, we need the following information:

Angle A in triangle rxby is congruent to angle A in triangle rzay.

Side rx is congruent to side rz.

Angle B in triangle rxby is congruent to angle B in triangle rzay.

By satisfying these conditions, we can conclude that triangles rxby and rzay are congruent.