Question

Complete the proof by supplying the reasons.

Given: AB= DC, AD= BC
Prove: Angle A = Angle C

Answer 1

To prove that Angle A equals Angle C, we use the Side-Side-Side postulate by noting that AB = DC and AD = BC, which makes the triangles congruent, and thus their corresponding angles are equal.

Step-by-step explanation:

To prove that Angle A is equal to Angle C, we can use the properties of congruent triangles. The information given states that AB = DC and AD = BC. By the Side-Side-Side postulate (SSS), if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. If the triangles are congruent, all their corresponding angles must also be congruent. Therefore, Angle A in one triangle would be congruent to Angle C in the other congruent triangle.

1. AB = DC (Given)
2. AD = BC (Given)
3. Triangle ABD is congruent to Triangle CDB by SSS postulate.
4. Angle A = Angle C (Corresponding angles of congruent triangles are equal)