Chapter 4.5, Problem 10PPS

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:

  $\begin{array}{l}\overline{MS}\cong \overline{RQ}\\ \overline{MS}\parallel \overline{RQ}\end{array}$

Proof:

From the given figure:

  

The two-column proof is written as:

No.	Steps of proof	Reason
1	$\begin{array}{l}\overline{MS}\cong \overline{RQ}\\ \overline{MS}\parallel \overline{RQ}\end{array}$	Given information
2	$\angle SPM\cong \angle QPR$	The vertical angles are always congruent in nature
3	$\angle SMP\cong \angle QRP$	According to the alternative internal angle theorem
4	$\Delta MSP\cong \Delta RQP$	According to angle side angle (ASA) congruence postulate

Hence proved