Question

no diagram given: PX and QY are altitudes of acute triangle PQR, and Z is the midpoint of PQ. Prove that XYZ is isosceles.

Answer 1

Do you have to prove by postulates and theorems? if so I don't have those memorized but I would start with a picture to help you visualize what the problem looks like. It always helps me.

Answer 2

Thanks - Yes - need postulates, but don't worry about that, we can figure that out. We did draw picture like yours, but can't figure out the next steps for isosceles. Which sides are congruent?

Answer 3

You only need to know that the mid point of the hypotenuse of a right triangle is equidistant from the triangle vertices

Answer 4

which midpoint of which triangle though?

Answer 5

Got it now, I think...

Answer 6

According to your question, you are only given one mid-point

Answer 7

Very simple, once you know this fact..

Answer 8

Thanks!!