A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality o

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A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality of corresponding sides of similar triangles to establish that a^(2)+b^(2)=c^(2).

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