Question

Prove that the angle bisector of the angle opposite to the base of an isosceles triangle is also the altitude to the base

Answer 1

Given:
.. apex angle is divided into 2 equal parts
.. base angles are equal
.. side lengths are equal
1. The triangles are congruent by ASA
2. The angles where the bisector meets the base add to 180°. (They are linear angles formed by the bisector and the base.)
3. The angles where the bisector meets the base are congruent. (The are corresponding angles of congruent triangles.
4. The angles where the bisector meets the base are 90°. (Congruent angles that add to 180° must be 90°.)
5. The bisector is a line from the apex meets the base at a right angle, so is an altitude. (Definition of altitude.)