Prove the Following:

Question

Given: Triangle ABC with AC = BC. The bisectors of the base angles, angle A and angle B, intersect each other at F. Prove that line CF is perpendicular to segment AB. (It is not necessary to use any congruent triangle in this proof.)

Answer 1

For any triangle, the intersection of two angle bisectors defines bisecting the third angle by connecting third vertex (C in this instance) to the intersection (F in this case). ABC is isosceles, with AB as base. Bisect the angle opposite of base in isosceles triangle creates a line perpendicular to the base (and bisects the base itself). It is a provable property for all isosceles triangles.