Prove that in an isosceles triangle the two heights drawn from the vertices of the base are equal.

Sign of equality of right-angled triangles: If the hypotenuse and acute angle of one right-angled triangle are respectively equal to the hypotenuse and acute angle of another right-angled triangle, then such triangles are equal.

Δ AMB = Δ BKС, because angle AMB = angle BKС – as angles at the base of an isosceles triangle.

AB – is the hypotenuse and Δ AMB and Δ BKС.

If the triangles are equal, then their corresponding legs are also equal, AM = K, MB = AK.

MB = AK – these are our heights.




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