Question

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

Answer 1

(Adding to the other person's answer)

For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.

It won't work to just say something like the def. of parallelograms.

Answer 2

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)