Two acute triangles with the same height as the third side are congruent.

It is known that AB=DE, BC=EF, high BM, = high EN.

Prove that all triangles ABC are equal to triangles DEF

In a right triangle, ABM, DEN, AB=DE and BM=EN.

So the right triangle ABM is equal to the right triangle DEN(HL).

So angle A= angle d

In the right triangle BCM, EFN, BC=EF, BM=EN.

So the right triangle BCM is equal to the right triangle EFN(HL)

So angle C= angle f

In a triangle, ABC is equal to triangle DEF.

Angle A= angle d, angle C= angle f, BC=EF.

So triangle ABC is equal to triangle DEF(AAS)

So two acute triangles with the same height as the third side are congruent.