Prove that a triangle is isosceles if and only if two medians are congruent.

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- Sep 28th 2010, 02:27 PMMATNTRNGIsosceles Triangle Proof
Prove that a triangle is isosceles if and only if two medians are congruent.

- Sep 28th 2010, 02:50 PMPlato
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 PMMATNTRNG
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 AMTraveller
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 PMbjhopperisosce 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

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