Geometry help..PLEEEEASSE!!

[1cat2ferrets]

Ok, my son and I have had it with proving theorems.
Any Geometry whizzes out there please help us write the proof for this:

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: triangle ABC is isosceles; line CD is the altitude of base line AB.
To prove: line CD bisects angle ACB
Plan: ?????

Thanks for any help at all!

[forty-two]

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: triangle ABC is isosceles; line CD is the altitude of base line AB.
To prove: line CD bisects angle ACB

Here's my stab:

Line CD is perpendicular to line AB, by the definition of altitude (The height of a triangle is the straight line drawn from the vertex perpendicular to the base).
Then angle CDA and angle CDB are 90 deg, b/c perpendicular lines form right angles.
Angle CAD is equal to angle CBD, b/c in an isosceles triangle the angles at the base are equal.
Triangle CAD is congruent to triangle CBD, by the Angle-Angle-Side Theorem (if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the two triangles are congruent).
Angle ACD is equal to angle BCD, by the def of congruent triangles.
Since angle ACD is equal to angle BCD, line CD bisects angle ACB, by def of an angle bisector (a ray that is in the interior of an angle and forms two equal angles with the sides of that angle).

This is the first time I've done geometry in 12 years, and I relied heavily on an online definitions page and a theorems page, so it might not be the best way (or even right), but I hope it helps. Depending on how your geometry program introduces theorems, it might expect you to prove some/all of the theorems I used because they haven't been proven in your program yet. Or it might have taken an entirely different approach.

[Caroline]

The proof from the above poster is great. You could also use the third angles theorem which says that if two angles of one triangle are congruent to two angles of another triangle, then their third angles are congruent. You would use this in place of the angle-angle-side triangle congruence theorem.

I taught this proof today.

[1cat2ferrets]

for the Geometry help. I had Geometry ages ago and my brain is extremely tired!