Question

Given: Quadrilateral PAST, TX = AX; TP || AS Prove: Quadrilateral PAST is a parallelogram.

Answer 1

1) Quadrilateral PAST, TX=AX, $\overline{TP} \parallel\overline{AS}$ (given)

2) $\angle XPT \cong \angle XSA$ and $\angle XTP \cong \angle XAS$ (alternate interior angles theorem)

3) $\triangle TXP \cong \triangle AXS$ (AAS)

4) $\overline{TP} \cong \overline{AS}$ (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)