Problem 67 from Kiselev's Geometry,
Prove that in an isosceles triangle, two medians are congruent, two angle bisectors are congruent, two altitudes are congruent.
Here is the content page in the book. The problem belongs to Chapter 1.5.
The theorems covered in chapter 1.5 are,
(i) In an isosceles triangle, the bisector of the angle at the vertex is at the same time the median and the altitude.
(ii) In an isosceles triangle, the angles at the base are congruent.
(iii) In an isosceles triangle, the bisector of the angle at the vertex is an axis of symmetry of the triangle.
I have understood the proof for these theorems and I have tried to use these theorems and others mentioned in previous chapters to prove the theorem in problem 67, but I can't prove it.
Please help. Also, please avoid using theorems that are covered in the later part of the book. :)