Question

1. angle bde is congruent to angle bac. \\( \angle bde \cong \angle bac \\) name another pair of congruent angles. explain how you know.

Explanation:

Step1: Identify the relationship between lines

Assume line \(m\) is parallel to line \(l\).

Step2: Use the property of parallel lines and transversal

When two parallel lines (\(m\) and \(l\)) are cut by a transversal (\(AC\) and \(BC\) are related to the angles in question). For \(\angle BED\) and \(\angle BCA\), since \(m\parallel l\) (assumed based on the congruence of \(\angle BDE\) and \(\angle BAC\) which is a case of corresponding angles), by the corresponding - angles postulate, if two parallel lines are cut by a transversal, then corresponding angles are congruent.

Answer:

\(\angle BED\cong\angle BCA\). Because if we assume line \(m\) is parallel to line \(l\) (since \(\angle BDE\cong\angle BAC\) which are corresponding angles), and when two parallel lines are cut by a transversal \(BC\), \(\angle BED\) and \(\angle BCA\) are corresponding angles. So \(\angle BED\cong\angle BCA\) by the corresponding - angles postulate.