SOLUTION: (given) triangle ABC is isosceles; line CD is the altitude to base line AB (to proove) line CD bisects angle ACB

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Question 123804: (given) triangle ABC is isosceles; line CD is the altitude to base line AB
(to proove) line CD bisects angle ACB
Answer by ilana(307) About Me  (Show Source):
You can put this solution on YOUR website!
I usually hate Geometry proofs, but this one is fun! Since CD is an altitude, it meets AB perpendicularly, forming 2 right angles. So it splits triangle ABC into two right triangles. Since triangle ABC is isosceles, angle A is congruent to angle B (call that measure x. So both of these triangles have 1 angle measuring 90 degrees and 1 measuring x degrees. So the remaining angle must be 180-(90+x), or (90-x)degrees. So angle DCB is congruent to angle DCA, so CD bisects angle ACB. If you need a formal proof, you need to look in your book and find those theorems and definitions for wording and details. (Now I remember... that is the part I don't like!) Good luck!