Question

the figures are congruent. match the corresponding angles and the corresponding sides.
∠a
∠b
∠c
∠d

Explanation:

Step1: Identify congruent figures' correspondence

When two figures are congruent, their corresponding parts (angles and sides) are equal. We assume the correspondence of the polygons. Let's match the angles based on the order of vertices.

Step2: Match angle \(A\)

Looking at the first polygon \(ABCD\) and the second polygon \(FEHG\). If we assume \(A\) corresponds to \(F\) (by visual inspection of the shape and congruence), \(\angle A=\angle F\)

Step3: Match angle \(B\)

If we assume the order of vertices for congruence (e.g., \(ABCD\cong FEHG\)), then \(\angle B\) corresponds to \(\angle E\) (by the structure of the polygons, the angles at the non - parallel sides in the trapezoid - like shape)

Step4: Match angle \(C\)

\(\angle C\) corresponds to \(\angle G\) (as the last non - right angle in the first polygon and the non - right angle in the second polygon)

Step5: Match angle \(D\)

\(\angle D\) corresponds to \(\angle H\) (as the right angles in the first polygon and the right angles in the second polygon)

Answer:

\(\angle A-\angle F\), \(\angle B - \angle E\), \(\angle C-\angle G\), \(\angle D-\angle H\)