Geometry Proofs : Triangles and Internal and External Bisectors; Length of Altitude ( Height) and Isoceles Triangles

1- If we have a triangle ABC, then prove that the internal and external bisectors of the angle of a triangle are perpendicular (assume for angle A)

2- Prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles.