Question

given: $\triangle abc$ with $\overline{pq} \parallel \overline{bc}$
complete the sentences.
it was given that $\overline{pq} \parallel \overline{bc}$, then $\angle apq \cong \angle abc$ since corresponding angles formed by parallel lines cut by a transversal are congruent.
by the reflexive property of congruence, $\angle a \cong \angle a$ therefore, $\triangle apq \sim \triangle abc$ using (select)

Explanation:

Step1: Identify congruent angles

We know $\angle APQ \cong \angle ABC$ (corresponding angles from parallel lines $\overline{PQ} \parallel \overline{BC}$) and $\angle A \cong \angle A$ (Reflexive Property of Congruence).

Step2: Apply similarity criterion

When two pairs of corresponding angles of two triangles are congruent, the triangles are similar by the AA (Angle-Angle) Similarity Postulate.

Answer:

AA (Angle-Angle) Similarity Postulate