I was given a proof for my geometry work today and, upon further investigation, I think I found a way to solve it pretty easily. Here is the "problem" (I still call them math problems): (Can't post images but there is a diagram of an isosceles triangle)
Given: $\triangle ABD$ is isosceles with long side BD. $AC \perp BD$
Prove: $C$ is the Midpoint of $BD$.
Okay so this is the way I would like to solve this (not that it really matters because the teacher gave me a specific way he wanted me to solve it, but I want to know if I'm right):
Statement: $\triangle ABD$ is an isosceles triangle
Reason: Given
Statement: $AC \perp BD$
Reason: Given
Statement: C is the Midpoint of BD
Given: Def. Of a bisector
Is this correct? I feel like it should be since the definition of a bisector is: A line, ray or segment which cuts another linesegment into two equal parts.
Thanks!