Chapter 3.2, Problem 11PSA

To determine

To prove : The congruency of $\Delta NOP\cong \Delta SRP$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle N$ is complementary to $\angle NPO$

  $\angle S$ is complementary to $\angle SPR$

  $\angle NPO\cong \angle SPR$

  $\overrightarrow{NP}\cong \overrightarrow{SP}$

Formula used : The following formulas have been used

Complementary angles of congruent angles are congruent

If two angles and a side between them are congruent in any two triangles, then the triangles are said to be congruent

Proof : As we know that

  $\angle N$ is complementary to $\angle NPO$

  $\angle S$ is complementary to $\angle SPR$

And

  $\angle NPO\cong \angle SPR$ ,

Thus, we can say that

  $\angle PNO\cong \angle PSR$

Also,

  $\overrightarrow{NP}\cong \overrightarrow{SP}$ is given

Thus, by SAS property mentioned above, the two triangles are said to be congruent