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.