I need proofs and a drawing for both (a) and (d). Please WRITE the solution in reason statement format.

13. Prove each of the following: (a) The median to the base of an isosceles triangle bisects the vertex angle. (b) If the bisector of an angle of a triangle is also an altitude to the opposite side, then the other two sides of the triangle are congruent. (c) If a median to a side of a triangle is also an altitude to that side, then the triangle is isosceles. (d) In an isosceles triangle, the medians to the legs are congruent. (e) In an isosceles triangle, the bisectors of the base angles are congruent