parallelo

[maihuna]

In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS

[DanaJ]

I pretty sure that stmt 2 by itself is not sufficient, since I immediately thought of an isosceles trapezoid with PQ and SR as the un-parallel sides. But I cannot think of an explanation for why stmt 1 is enough.... Although I'm confident it has to do with the angles that the two parallel sides create with a digonal that, together with the lengths of the sides, make similar triangles...

[sachinkr]

IMO the ans is A

Given PQRS is qualilateral whose sides PQ || RS.
We need to find whether PQRS is a parallelogram?

A: PQ = SR, Sufficient (Condition for parallelogram is 2 opposite sides of quadilateal are parallel and equal)

B: PS = QR , not sufficient as mentioned by DanaJ.

[Freedom007]

but PQRS can very easily be a square and still satisfy statement (1) so why is the answer not E?

[piyush_nitt]

but PQRS can very easily be a square and still satisfy statement (1) so why is the answer not E?

Square is a ||gram.