Question

For the following figure, given that $▱PQRS;PA=RB$then prove that$AS=BQ$ .

Short answer

Thus, the statement is $AS=BQ$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the SAS postulate.

SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Step 3- Step description.

Consider the triangles$PAS$ and $RBQ$.

Consider$PA=RB$ .

Use the definition of parallelogram such that

$\begin{array}{l}PS=RQ\\ \angle P=\angle R\end{array}$

Use the SAS postulate that implies that $\Delta PAS\cong \Delta RBQ$.

As the corresponding parts of congruent triangles are congruent thus the sides are congruent such that$AS=BQ$ .

Therefore $AS=BQ$.