As shown in the figure, in the triangle ABC, CD is the height on the side of AB, and the square of CD = ad * BD. try to explain that the triangle ABC is a right triangle

Proof: because CD is the height of triangle ABC
So angle BDC = angle CDA = 90 degrees
Because CD ^ 2 = ad * BD
So CD / BD = ad / CD
So triangle BDC is similar to triangle CDA
So angle B = angle ACD
Because angle B + angle BDC + angle BCD = 180 degrees
So angle B + angle BCD = 90 degrees
So angle ACD + angle BCD = angle ACB = 90 degrees
So the triangle ABC is a right triangle

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