Chapter 5.6, Problem 2PSA

To determine

To prove: QuadrilateralRSTV is a parallelogram.

Explanation of Solution

Given information:In quadrilateralRSTV,

  $\angle XRV\cong \angle RST$ ……………………. (i)

  $\angle RSV\cong \angle TVS$ ……………………. (ii)

Concept used: If both pair of opposite sides are parallel to each other then the quadrilateral is a parallelogram.

Proof:From the given diagram it is clear that $\angle XRV$ and $\angle RST$ are the corresponding angles where XS is a traversal for lines RV and ST , these corresponding angles are congruent as per equation (i) then it means,

  $RV\parallel ST$

Also, $\angle RSV$ and $\angle TVS$ are alternate interior angles for lines TV and SR where VScan be a traversal, these alternate interior angles are congruent as per equation (ii) then it means,

  $TV\parallel SR$

Hence, both pairs of opposite sides are parallel to each other so the given quadrilateral RSTVis a parallelogram.