Question

OM is an altitude of triangle OPQ and PM = MQ Prove that angle POM = Angle QOM​

Answer 1

Angle POM = Angle QOM in a right triangle

Here is one way to prove that angle POM = angle QOM in triangle OPQ, where OM is the altitude of the triangle and PM = MQ:

• Draw the altitude of triangle OPQ, which is OM.

• Draw a line segment PM, which is equal to MQ.

• Now we have two right triangles, POM and QOM, which share a hypotenuse of OM and have legs PM and MQ respectively.

• Since PM = MQ, these two legs are congruent.

• By the converse of the Pythagorean theorem, if the legs of a right triangle are congruent, then the angles opposite to those legs are congruent.

• Therefore, angle POM = angle QOM.

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