Chapter 4.5, Problem 9PPS

To determine

To prove:

  $\Delta UVY\cong \Delta XVW$ for the following figure in the form of the two-column:

  

Explanation of Solution

Given information:

  $\overline{UY}\parallel \overline{XW}$

  $V$ is midpoint of $\overline{YW}$

Proof:

From the given figure:

  

The two-column proof is written as:

No.	Proof of steps	Reason
1.	$\overline{UY}\parallel \overline{XW}$	Given information
2.	$V$ is midpoint of $\overline{YW}$	Given information
3.	$\overline{YV}\cong \overline{VW}$	According to the midpoint theorem
4.	$\begin{array}{l}\angle VWX\cong \angle VYU\\ \angle VUY\cong \angle VXW\end{array}$	According to the alternative internal angle theorem
5.	$\Delta UVY\cong \Delta XVW$	According to angle side angle (ASA) congruence postulate

Hence proved