Question

if a translation maps ∠d onto ∠b, which of the following statements is true? △ced - △cab △ced - △cba $overline{ce}cong2overline{ca}$ $overline{cd}cong2overline{cb}$

Explanation:

Step1: Recall similarity - criteria

If a translation maps ∠D onto ∠B, then ∠D = ∠B. Also, ∠C is common to both △CED and △CAB.

Step2: Apply AA (Angle - Angle) similarity

By the AA similarity criterion (two angles of one triangle are equal to two angles of another triangle), △CED∼△CAB.

Step3: Analyze side - length relationships

There is no information given to suggest that \(\overline{CE}\cong2\overline{CA}\) or \(\overline{CD}\cong2\overline{CB}\).

Answer:

△CED∼△CAB