Chapter 3.2, Problem 5PSA

To determine

To prove : The congruency of $\Delta MRO\cong \Delta PRO$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{RO}\perp \overrightarrow{MP}$

  $\overrightarrow{MO}\cong \overrightarrow{OP}$

Formula used : Two triangles are congruent by Side-angle-side property, if there are two congruent sides, and the angle between them is also congruent

Proof : we know that $\overrightarrow{RO}\perp \overrightarrow{MP}$ , so from this information we can say that

  $\angle ROM\cong \angle ROP\cong {90}^0$

Now, we can also see that there is a common side RO between them. Hence, now we can say that

  $\angle ROM\cong \angle ROP$

  $\overrightarrow{MO}\cong \overrightarrow{OP}$

  $\overrightarrow{RO}\cong \overrightarrow{RO}$

Thus, now by using the SAS property as mentioned above, we can say that two triangles are congruent

Hence, proved that $\Delta MRO\cong \Delta PRO$