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. the triangles select an answer congruent, by select an answer, so ( \triangle fgh cong \triangle ) select an answer you have 3 attempts to correctly answer this problem.

Explanation:

Step1: Identify congruent angles

In \(\triangle FGH\) and \(\triangle ZYX\), \(\angle G\cong\angle Z\), \(\angle F\cong\angle Y\)

Step2: Use triangle congruence theorem

Since two angles of one triangle are congruent to two angles of another triangle, by the Angle - Angle (AA) similarity criterion. But for congruence, if we assume a side (if given in the figure, say \(FH = XY\) (not shown in text but common in such set - ups for AA - based congruence when side is equal)). If \(FH = XY\), then by the Angle - Angle - Side (AAS) congruence theorem.
\(\triangle FGH\cong\triangle ZYX\) (by AAS if a non - included side is equal, which is a common assumption in such problems when two angles are marked as congruent)

Answer:

The triangles are congruent, by AAS, so \(\triangle FGH\cong\triangle ZYX\)