Question

A C B, X Z Y

Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement.
If no, justify your answer.

Answer 1

Yes.

∆CAB ≅ ∆XYZ by AAS Congruence Theorem.

Explanation:

There's enough information provided in the diagram above for us to prove that ∆CAB is congruent to ∆XYZ.

From the diagram, we cam observe the following:

<A ≅ <Y

<B ≅ <Z

side CA ≅ XY

Using the Angle-Angle-Side (AAS) Congruence Theorem, since two angles, <A and <B, and a non-included side, CA, in ∆CAB are congruent to two the corresponding angles, <X and <Z, and a non-included side, XY, in ∆XYZ, then ∆CAB is congruent to ∆XYZ.