Two Column Proof For a Triangle (Really really need help!)

[lilflutterby]

I am having a trouble figuring out proofs. Here is one that I'm having problems with in particular.

Given: Triangle PDQ, line DM is an altitude and a median.
To Prove: Triangle PDQ is isosceles.

So yeah, I have no clue how to write a two column proof for that problem. Any help is appreciated. Thanks!

 

[tkhunny]

Re: Two Column Proof For a Triangle (Really really need help

I am having a trouble figuring out proofs. Here is one that I'm having problems with in particular.

Given: Triangle PDQ, line DM is an altitude and a median.
To Prove: Triangle PDQ is isosceles.

What do you need to prove isosceles? DP = DQ right? Think on that as you extract information from the clues.

DM is an median -- Aha! Then PM = QM
DM is an altitude -- Aha! Then angle(DMP) = angle(DMQ) = 90º - a right angle

Say, can we use some right triangle stuff here? Maybe the pythagorean theorem. No, we would need that other side. Wait.

DM = DM -- That's reflexive.

We have Side-Angle-Side and we have corresponding parts of congruent triangles. We didn't need the Pythagorean Theorem after all.

It's a thought process, not a check list.