Question

1. elena needs to prove angles bed and bca are congruent.

∠bde ≅ ∠bac
provide reasons to support each of her statements.
a. line m is parallel to line ℓ.
b. angles bed and bca are congruent.

Explanation:

a. Since \( \angle BDE\cong\angle BAC\), by the converse of the corresponding angles postulate (if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel), line \(m\) is parallel to line \(\ell\).
b. Because line \(m\) is parallel to line \(\ell\) (from part a), by the corresponding angles postulate (if two parallel lines are cut by a transversal, then the corresponding angles are congruent), \(\angle BED\) and \(\angle BCA\) are congruent.

Answer:

a. Converse of the corresponding angles postulate.
b. Corresponding angles postulate.