Question

(a) problem 11: (first taught in lesson 23) given that $overline{ed}paralleloverline{ab}$, select which type of angle pair $angle d$ and $angle a$ are and then tell whether the angles are congruent or supplementary.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines (ED || AB) are cut by a transversal (in this case, the line that passes through points C), alternate - interior angles are formed.

Step2: Identify the angle pair

∠D and ∠A are located between the parallel lines ED and AB and on opposite sides of the transversal. So they are alternate - interior angles.

Step3: Determine congruence

By the alternate - interior angles theorem, when two parallel lines are cut by a transversal, alternate - interior angles are congruent. So ∠D and ∠A are congruent.

Answer:

∠D and ∠A are alternate - interior angles; congruent