Given SV//TU and SVX=UTX
Prove: VUTS is a parallelogram
Write a paragraph proof.
To prove that VUTS is a parallelogram, we need to show that its opposite sides are parallel. First, we are given that SV and TU are parallel, which means that angles SVX and TUX are congruent since they are corresponding angles. Additionally, we are given that SVX = UTX, which implies that angles SVX and UTX are congruent. From these congruent angles, we can conclude that angles UXT and VXS are congruent since they are corresponding angles with respect to parallel lines SV and TU.
Next, by the Transitive Property of Congruence, we can infer that angles UXT and VXS are congruent to angles SVX and TUX, respectively. Since angles SVX and TUX are congruent, and angles UXT and VXS are congruent, we can conclude that VUTS is a parallelogram based on the definition of a parallelogram - a quadrilateral with both pairs of opposite sides parallel. Therefore, VUTS is indeed a parallelogram.