Chapter 6, Problem 5CR

To determine

To prove : The congruency of $\angle TXV\cong \angle VAT$

Explanation of Solution

Given information : The following information has been given

TVAX is a rectangle

Formula used : Corresponding angles of any congruent polygons are congruent

Proof : We know that in triangles XTV and AVT,

  $\overrightarrow{XT}\cong \overrightarrow{AV}$ and TV is a common line.

Now, all angles of a rectangle are equal, thus,

  $\angle XTV\cong \angle AVT$

Hence, now we can say that triangles XTV and AVT are congruent by SAS.

Also, we know that the Corresponding angles of any congruent polygons are congruent. Thus, we can say that

  $\angle TXV\cong \angle VAT$ by virtue of congruency