# Isosceles Triangle Proof

• Sep 28th 2010, 02:27 PM
MATNTRNG
Isosceles Triangle Proof
Prove that a triangle is isosceles if and only if two medians are congruent.
• Sep 28th 2010, 02:50 PM
Plato
The basic idea behind this proof is that in two right triangles if the hypotenuses are congruent and two legs are congruent then the triangles are congruent.
• Sep 28th 2010, 06:12 PM
MATNTRNG
I was able to use that idea to prove that a triangle is isosceles iff its altitudes are congruent but medians? What hypotenuse? I am having trouble with the part of the proof where I am assuming that the medians are congruent.
• Sep 29th 2010, 02:06 AM
Traveller
A different approach involves the fact that the centroid divides any median in the ratio 2:1. Suppose in triangle ABC, the medians AD and BE are equal and intersect at centroid G. Can you use the fact above to prove something about triangles AGE and BGD ?
• Oct 1st 2010, 05:26 PM
bjhopper
isosce les triangle proof
posted by MATNTRNG
1 atriangleABC has a base BC and two rays AB andAC. midpoints of AB=M of AC =N
2 BN = CM given
3 MN is parallel to BC ( similar triangles )
4 arcs are drawn at B and C of equal lenghts ( median lenght)
5 a line parallel to BC is drawn above BC meeting arcs at M and N
6 MNCB is a trapezoid
7BN and CM are the trapezoid diagonals which are equal 4 above
8 MNCB is a regular trapezoid
9 a regular trapezoid is a truncated isosceles triangle
BM and CM extended meet at A the apex of isoscelesABC

bjh