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In a right angle triangle, the square of, hypotenuse side is equal to the sum of, squares of the other two sides., , , , Perpendicula, , , , e Pythagoras Theorem, (Hypotenuse)? = (Perpendicular)? + (Base)?, , e Proof, , Given : A right angle triangle ABC, right angle, at B., , , , To prove : (AC) 2 = (AB) 2 + (BC) ?, , Construction : Draw a perpendicular line BD, meeting AC at D., , Cc, , , , Proof :, , We know that, AABD ~ AABC, , Therefore, AD/AB =AB/BC ( corresponding, side's of similar triangle), , Or, (AB) 2 = (AD) X(AC)....csescssesseseseeeseeeseeees (1), Also, ABDC ~ AABC, , Therefore, CD/BC = BC/AC ( corresponding, side's of similar triangle), , Or, (BC) 2 = (CD)X(AC). ...seeeseessstessseeestsessteenees (2), Adding the equation (1) and (2) we get,, , (AB) 2 + (BC) 2 = (AD)x(AC) + (CD)x(AC), , (AB) ? + (BC) 2 = (AC) x (AD + CD), , Since, AD + CD = AC, , Therefore, (AC)? = (AB) 2 + (BC) 2, , Hence, the Pythagoras theorem is proved., , ¢ Application of Pythagoras, Theorem., , 1. To know if the triangle is a right - angle, triangle or not., , 2. Inaright angle triangle, we can, calculate the length of any side if the, other two sides are given., , 3. To find the diagonal of a square., , 2021-12-23