Question

2. Given: ZMOP is a right angle RP I OP Prove: MO || RP

Answer 1

Given that;

`\begin{gathered} \measuredangle MOP\text{ is a right angle.} \\ \measuredangle MOP=90^0 \end{gathered}`

And;

`\vec{RP}\perp\vec{OP}`

Since line RP is perpendicular to line OP, Angle RPO must be a right angle.

`\measuredangle RPO=90^0`

Recall that for two parallel lines intersected by a straight line, Same side interior angles are supplementary.

`A+B=180^0`

So, for line MO to be parallel to line RP, the sum of angle MOP and angle RPO must be equal to 180 degree.

`\measuredangle MOP+\measuredangle RPO=90+90=180^0`

Since the sum of angle MOP and angle RPO is equal to 180 degree, then line MO is parallel to line RP.

`\begin{gathered} \text{ Since} \\ \measuredangle MOP+\measuredangle RPO=180^0 \\ \text{Then;} \\ MO\Vert RP​ \end{gathered}`

Proved