Question

figure 1 and figure 2 below are congruent. which angle corresponds to angle c?

Explanation:

Step1: Recall congruent figures property

Congruent figures have corresponding angles equal, and corresponding vertices are in the same order.

Step2: Identify vertex correspondence

In Figure 1 (C, F, D, E) and Figure 2 (J, I, H, K), by matching the shape and vertex order, angle at C (in Figure 1) corresponds to angle at J (in Figure 2) as the vertices align in the congruent triangles' structure. Wait, no, let's re - examine. Wait, Figure 1: points C, F, D, E? Wait, no, looking at the figures, Figure 1 has points C, F, D (with E on FD) and Figure 2 has J, I, H (with K on IH). Wait, the congruent triangles: let's see the sides. The side CF in Figure 1 should correspond to JI in Figure 2, CD to JH, and FD to IH. So the angle at C (between CF and CD) should correspond to the angle at J (between JI and JH). Wait, no, maybe I misread. Wait, Figure 1: C, F, D – triangle? Wait, Figure 1: C connected to F and D, F connected to D (with E on FD). Figure 2: J connected to I and H, I connected to H (with K on IH). So the angle at C (∠C) is between CF and CD. In Figure 2, the angle at J (∠J) is between JI and JH. Since the figures are congruent, corresponding angles: ∠C corresponds to ∠J? Wait, no, maybe the labels: Let's check the order. If Figure 1 is triangle CFD (with E on FD) and Figure 2 is triangle JIH (with K on IH), then the correspondence is C ↔ J, F ↔ I, D ↔ H. So angle C (at vertex C) corresponds to angle J (at vertex J). Wait, but maybe I made a mistake. Wait, looking at the coordinates (even though not given, the shape): Figure 1: C is at the bottom - left of its triangle, F above C, D at the bottom - right. Figure 2: J is at the bottom - left of its triangle, I above J, H at the bottom - right. So yes, angle at C (bottom - left vertex) corresponds to angle at J (bottom - left vertex of the congruent triangle).

Answer:

Angle \( J \) (or \( \angle J \)) corresponds to angle \( C \) (or \( \angle C \)).