Question

ks
step statement reason

1. (overline{es}paralleloverline{hp}) given
2. (angle qescongangle qhp) corresponding angles are congruent

3.

1. (\triangle hqpsim\triangle eqs) angle - angle (aa) similarity theorem

Explanation:

Step1: Identify the common angle

$\angle Q$ is common to both $\triangle HQP$ and $\triangle EQS$.

Step2: Use AA similarity criterion

Since $\angle QES\cong\angle QHP$ (from step 2 in the given table) and $\angle Q=\angle Q$ (common angle), by the Angle - Angle (AA) similarity theorem, $\triangle HQP\sim\triangle EQS$.

Answer:

The reason for step 3 is that $\angle Q$ is common to both triangles. So the statement for step 3 is $\angle Q\cong\angle Q$ (Common Angle).