Question

directions: for each triangle pair drawn, write the parts and pieces you know to be congruent. if there is enough information for proof, write a triangle congruence statement and the theorem that proves the two triangles are congruent. proof:

the triangles congruent, by , so

Explanation:

Step1: Identify congruent angles

From the diagram, we can see that \(\angle G\cong\angle Y\) (marked with two - arc symbols) and \(\angle F\cong\angle X\) (marked with one - arc symbol).

Step2: Use the Angle - Angle - Side (AAS) congruence theorem

If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
We assume that \(GF = YX\) (if we consider the non - included side for the two pairs of congruent angles \(\angle G\cong\angle Y\) and \(\angle F\cong\angle X\)).
By the AAS (Angle - Angle - Side) congruence theorem, \(\triangle FGH\cong\triangle XZY\)

Answer:

\(\boxed{\angle G\cong\angle Y}\), \(\boxed{\angle F\cong\angle X}\), \(\boxed{\text{are}}\), \(\boxed{\text{AAS}}\), \(\boxed{XZY}\)