Triangle proof using no congruent triangles to solve

[Lindsey8417]

If D is the midpoint of line segment BC and line AD is perpendicular to line segment BC, prove that triangle ABC is isosceles. Do not use congruent triangles in your proof.[/code][/list]

 

[tkhunny]

We know

BD = CD - Definition of Midpoint
AD = AD - Reflexive
Triangle ADB is a Right Triangle
Triangle ADC is a Right Triangle

Using the Pythagorean Theorem

BD²+AD² = AB²
CD²+AD² = AC²

After a little algebra, AB = AC
One more statemet to make.

 

[zerodegrees]

Segment AD is a perpendicular bisector. Isn't there a corollary for perpendicular bisectors and isoceles triangles?