Thread: I think I have really messed this proof up! Please help!

My assignment was simple: prove that a triangle whose base angles are the same is an isosceles. But then I found out I cannot use the base angle theorem.

Now I found out that I have included unecessary info or else left out a step, my instructor didn't say for sure.

Does any one have any ideas on an easy way to fix my proof/diagram? Or do you think I should just start over trying to prove it from a different way.

My diagram and proof are attached.

Thank you!

Originally Posted by e-mom

My assignment was simple: prove that a triangle whose base angles are the same is an isosceles. But then I found out I cannot use the base angle theorem.

Now I found out that I have included unecessary info or else left out a step, my instructor didn't say for sure.

Does any one have any ideas on an easy way to fix my proof/diagram? Or do you think I should just start over trying to prove it from a different way.

My diagram and proof are attached.

Thank you!

First, why this didn't work.
1) You proved that the wrong pair of sides were equal. (We need AB=AC, you had AB=BC).
2) The reason this failed was the assumption that the perpendicular bisector of AC intersects the point B. This is not true in general. (Draw a more lopsided triangle and it should be clear.)

I would suggest that you bisected the wrong thing. I would start over with your triangle, bisect the angle A, and extend the bisector to intersect the line BC at point D. (Note: We canNOT assume BD=CD here. We would need to prove that.) The goal would then to be to prove that triangle ADB is congruent with triangle ADC. (Hint: Look for an angle-side-angle proof.)

-Dan

Prove it like this.
From the vertex draw an angle bisector. Now you have two triangles by a.a.s. and the proof it complete.

Thank you Perfect Hacker and Topsquark!

I will apply what you said as I refigure my crazy triangle!