Question

if a translation maps ∠e onto ∠a, which of the following statements is true? ∠b≅∠c ∠b≅∠d (overline{ce}congoverline{ca}) (overline{cd}congoverline{cb})

Explanation:

Step1: Recall translation property

A translation is a rigid - motion. Rigid motions preserve angle measures and segment lengths. If a translation maps ∠E onto ∠A, then the two triangles (△ECD and △ACB) are congruent. Corresponding angles of congruent triangles are congruent.

Step2: Identify corresponding angles

In congruent triangles △ECD and △ACB (by the translation mapping ∠E onto ∠A), ∠B and ∠D are corresponding angles. So, ∠B≅∠D.

Answer:

∠B≅∠D