Question

Given: SV II TU and SVX=UTX
Prove: VUTS is a parallelogram

Answer 1

In the given are SVX and UTX angles or triangles?

Answer 2

I think triangles

Answer 3

Ok. There are a few ways of proving parallelogram.
One way to prove a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.
Another way is to show that one pair of opposite sides is both parallel and congruent.
Since you have SV || TU, if you can show that seg SV is congr to seg VU, then you have a pair of opposite sides that is both parallel and congruent, and you can prove a parallelogram.
Since the triangles are congruent, seg SV and VU are congr by CPCTC. By given those segs are also parallel, so that proves the quadrilateral is a parallelogram.

Answer 4

Thank You sooo much!

Answer 5

Correction above: On line that starts Since you have SV || TU, ... seg SV congr to seg VU. I meant TU not VU.

Answer 6

It is given that SV and TU are congruent, this doesn't prove it's a parallelogram.