Question 21
a) Prove that if in a triangle there are two heights of equal length, then the triangle is isosceles.
b) Prove that if in a triangle there are two medians of equal length, then the triangle is isosceles.
c) On the sides $A B$ and $A C$ of a triangle $A B C$, choose two points $M, N$ such that $A M: A B=A N: A C$ and suppose that $B N=C M$; prove that the triangle $A B C$ is isosceles.
b) Prove that if in a triangle there are two medians of equal length, then the triangle is isosceles.
c) On the sides $A B$ and $A C$ of a triangle $A B C$, choose two points $M, N$ such that $A M: A B=A N: A C$ and suppose that $B N=C M$; prove that the triangle $A B C$ is isosceles.