SOLUTION: Could you please help me solve this geometric proof? I am trying to understand it, but I have no idea how to do this proof. Prove that if an angle bisector is also an altitude,

Algebra ->  Geometry-proofs -> SOLUTION: Could you please help me solve this geometric proof? I am trying to understand it, but I have no idea how to do this proof. Prove that if an angle bisector is also an altitude,      Log On


   

Question 932426: Could you please help me solve this geometric proof? I am trying to understand it, but I have no idea how to do this proof.
Prove that if an angle bisector is also an altitude, then the triangle is isosceles.
Given: Triangle ABC, with line BD an angle bisector and altitude line AC.
Prove: Triangle ABC is isosceles.
I would draw the figure for you, but I do not know how to draw it for you on here.
Thank you so much!!!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
BD is an altitude to AC, so
Also
By looking at right triangles BAD and BCD, it follows that (note that these two triangles are furthermore congruent).
Therefore triangle ABC is isosceles because two of its interior angles (BAD = BAC, and BCA) are equal.