Chapter 3.2, Problem 16PSA

To determine

To prove : The congruency of $\Delta NOT\cong \Delta RSP$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle R\cong \angle N$

  $\overrightarrow{RP}\cong \overrightarrow{NT}$

  $\overrightarrow{RT}\cong \overrightarrow{NP}$

  $\overrightarrow{TS}\cong \overrightarrow{OP}$

Formula used : If two sides and the angle between them are congruent for any two triangles, then the triangles are said to be congruent by SAS property

Proof : We know that

  $\overrightarrow{RT}\cong \overrightarrow{NP}$ , and

  $\overrightarrow{TS}\cong \overrightarrow{OP}$

Now, we subtract second equation from the first equation. Thus, we get

  $\overrightarrow{RS}\cong \overrightarrow{NO}$

Also, we have

  $\angle R\cong \angle N$

  $\overrightarrow{RP}\cong \overrightarrow{NT}$

Thus, we can say that $\Delta NOT\cong \Delta RSP$ by SAS property

Hence, given congruency is proved