SOLUTION: GIVEN: TRIANGLE ABC IS ISOSCELES; LINE SEGMENT CD IS THE ALTITUDE TO BASE OF LINE SEGMENT AB. PROVE: LINE SEGMENT CD BISECTS ANGLE ACB. I MADE THE PLAN BUT I DON'T THINK IT'S

Question 96735This question is from textbook geometry
: GIVEN: TRIANGLE ABC IS ISOSCELES; LINE SEGMENT CD IS THE ALTITUDE TO BASE OF LINE SEGMENT AB.
PROVE: LINE SEGMENT CD BISECTS ANGLE ACB.
I MADE THE PLAN BUT I DON'T THINK IT'S RIGHT BECAUSE I CAN NEVER FINISH THE PROBLEM CORRECTLY.
CAN YOU PLEASE PROVIDE ME WITH A PLAN. This question is from textbook geometry

Answer by mathslover(157) (Show Source): You can put this solution on YOUR website!
Given : triangle ABC is isosceles
CD is the altitude to the base of the triangle
to Prove: Line Segment CD bisects Angle ACB ie angle ACD = angle BCD
Proof:

In triangles ACD and BCD
AC = BC Sides of an isosceles triangle ABC
CD = CD Common side of the two triangles
angle ADC = BDC =90 given CD is the altitude to the base
therefore triangle ACD is Congruent to triangle BCD ( by the RHS theorem)

right angle-hypotunese-side
therfore AD=BD
and hence angle ACD = angle BCD angles opposite to the equal sides are also equal
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