Chapter 3.2, Problem 14PSA

To determine

To prove : The congruency of $\Delta NPR\cong \Delta NTS$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle 1\cong \angle 4$

  $\overrightarrow{PR}\cong \overrightarrow{TS}$

  $\overrightarrow{NP}\cong \overrightarrow{NT}$

Formula used : The following formulas have been used in the question

If two sides and the angle containing them are congruent for two triangles, then the triangles are said to be congruent by SAS rule

Two angles are congruent if their supplementary angles are congruent

Proof : We know that $\angle 1\cong \angle 4$ , thus, their supplementary angles will also be congruent. Hence,

  $\angle 2\cong \angle 3$

And, we also know that

  $\overrightarrow{PR}\cong \overrightarrow{TS}$

  $\overrightarrow{NP}\cong \overrightarrow{NT}$

Thus, we can say that $\Delta NPR\cong \Delta NTS$ by SAS rule

Hence, given congruency is proved