Question

AL is perpendicular to OP and AM is perpendicular to OQ such that AL= AM .show that OA bisects angle POQ .​

Answer 1

Given:

AL=AM

To prove:

angle QOA = angle AOP

Construction:

Join O and A

Proof:

In ΔAOL & ΔAOM, we have:

OA = AO [Common side]

angle ALO = angle AMO [each 90°]

AL = AM. [Given]

So by S-A-S congruent criterion, ΔAOL≈ΔAOM

Therefore, angel QOA= angle AOP