SOLUTION: I have to prove that Triangle ABC is isosceles.D is the midpoint at the base. Here is what I have so far: Given:Angle BAD is congruent to Angle CAD Given:Line segment AD is perp

Algebra ->  Geometry-proofs -> SOLUTION: I have to prove that Triangle ABC is isosceles.D is the midpoint at the base. Here is what I have so far: Given:Angle BAD is congruent to Angle CAD Given:Line segment AD is perp      Log On


   

Question 310134: I have to prove that Triangle ABC is isosceles.D is the midpoint at the base.
Here is what I have so far:
Given:Angle BAD is congruent to Angle CAD
Given:Line segment AD is perpendicular to Line segment BC
This is what I come up with myself:
Angle BDA is congruent to Angle CDA---Right Angle Theorem
Angle ADB is congruent to Angle ADC---Right Angle Theorem
Line segment AD is congruent to Line segment AD---Reflexive
Line segment BD is congruent to Line segment CD---Line segment AD is a midpoint of Line segment BC
Angle BAD is congruent to Angle CAD---Line segment AD is an angle bisector
Triangle ABD is congruent to Triangle ACD---ASA
Line segment AB is congruent to Line segment AC---CPCTC
Triangle ABC is isosceles---Line segment AD is perpendicular to Line segment BC and an angle bisector of Angle BAC
Apparently, there is quite a lot missing and I have not received any help from teachers, yours would be greatly appreciated!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"Given:Angle BAD is congruent to Angle CAD"

"Angle BDA is congruent to Angle CDA---Right Angle Theorem"

"Line segment AD is congruent to Line segment AD---Reflexive"

triangle BAD is congruent to triangle CAD---ASA

side BA is congruent to side CA---CPCTC

triangle ABC is isoc---definition


this is the essence of the proof
you may need to "touch up" a little