Chapter 8.3, Problem 5PSA

To determine

To prove : The similarity of $\Delta TVY$ with respect to $\Delta PXY$ .

Explanation of Solution

Given information : Here, we have given that TVPX is a trapezoid with $\overline{TV}$ and $\overline{XP}$ as bases.

Proof:

As, TVPX is a trapezoid,

  $\Rightarrow \overline{TV}\parallel \overline{XP}$

Now, as $\overline{TV}\parallel \overline{XP}$ ,

  $\Rightarrow \angle TVY\cong \angle YXP$ and $\angle VTY\cong \angle YPX$ (Alternate Interior Angles)

Now, In $\Delta TVY$ and $\Delta PXY$

  $\angle VTY\cong \angle YPX$ (Proved above)

  $\angle TVY\cong \angle YXP$ (Proved above)

  $\Rightarrow \Delta TVY\sim \Delta YPX$ (By AA Similarity Rule)