Question

Given: D is the midpoint of segment AC, segment ED is congruent to segment FD and angle EDA is congruent to angle FDC.Prove: angle A is congruent to angle C.

Answer 1

the Since D is the midpoint of AC, we can say that AD=DC, then the triangles ADE and CDF would be similar by the SAS theorem which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

If the triangles are congruent, their angles are equal.