Giorgos Giannoulakis
New member
- Joined
- Oct 4, 2022
- Messages
- 3
Consider a triangle [math]ABC[/math] and the bisector [math]AD[/math] of angle [math]A[/math]. Prove that: [math](AB>AC) \iff (BD>CD)[/math]
I am struggling with this problem. I am not allowed to use the angle bisector theorem with which of course it is solved very easily.
I was thinking that I need to use the fact that every exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Also the fact that if two angles of a triangle are unequal, then the measures of the sides opposite these angles are also unequal, and the longer side is opposite the greater angle.
Still though I cannot find a way to solve this
Can anyone help me?
Thanks!
I am struggling with this problem. I am not allowed to use the angle bisector theorem with which of course it is solved very easily.
I was thinking that I need to use the fact that every exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Also the fact that if two angles of a triangle are unequal, then the measures of the sides opposite these angles are also unequal, and the longer side is opposite the greater angle.
Still though I cannot find a way to solve this
Can anyone help me?
Thanks!