Question

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

Explanation:

Step1: Recall properties of translation

Translation is a rigid transformation. Rigid transformations preserve angle measures and side - lengths. If a translation maps \(\angle D\) onto \(\angle B\), then \(\triangle ECD\) is translated to \(\triangle ABC\).

Step2: Analyze angle congruence

In a translation, corresponding angles are congruent. For \(\triangle ECD\) and \(\triangle ABC\) (due to the translation mapping \(\angle D\) to \(\angle B\)), \(\angle E\) and \(\angle A\) are corresponding angles.

Answer:

\(\angle E\cong\angle A\)