SOLUTION: 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 segment CD is the a

Algebra ->  Geometry-proofs -> SOLUTION: 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 segment CD is the a      Log On


   

Question 339653: 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 segment CD is the altitude to the base segment AB
To Prove: Line segment CD bisects angle ACB
I really need some help with this.I have to write out a 2 column proof and a plan for the proof.I kinda have a proof but not sure if its right?
And I have no idea how to do a plan for the proof??? I don't remember learning that? PLEASE HELP me with the proof and the plan.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Plan:

The measures of AC and BC are equal because they are legs of isosceles triangle ABC.

Angles ADC and BDC are right angles because CD is an altitude, which is
perpendicular to the base.

The measure of CD is equal to itself.

Right triangles ADC and BDC are congruent because two right triangles are
congruent if the measures of the hypotenuse and a leg of one right triangle
are equal to the measures of the corresponding parts of the other right
triangle.

Angle ACD and Angle BCD have equal measures because they are corresponding
parts of congruent right triangles ADC and BDC.

CD bisects angle ACB because it divides the angle ACB into two angles with
equal measures, ACD and BCD. 

Now you can write the two-column proof.

Edwin