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

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      Log On


   

Question 209023This question is from textbook Geoemetry
: 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 AB
Could you help me solve this 2-column proof by using statements and reasons please?
This question is from textbook Geoemetry

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Given: Triangle ABC is isosceles; 
       Line segment CD is the altitude to the base AB

To prove: Angle ACD = angle BCD




angle A = angle B       Base angles of isosceles triangle

angle ADC = 90°         An altitude of a triangle is 
                        perpendicular to a side

angle BDC = 90°         An altitude of a triangle is 
                        perpendicular to a side

angle ADC = angle BDC   Both are right angles 

Angle ACD = angle BCD   If two angles of one triangle are
                        equal to two angles of another
                        triangle, the third angles are 
                        equal.

 Edwin