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What is inverse of Pythagoras theorem??? |
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Answer» Thanks for asking the question! ANSWER:: INVERSE PYTHAGORAS THEOREM To prove - If in a triangle the SQUARE on one of the SIDES equals the sum of the squares on the REMAINING two sides of the triangle, then the angle contained by the remaining two sides of the triangle is right. Proof - Let there be a triangle ABC BC² = BA² + AC² After this , draw AD at right angles to AC Make DA =AB Join DC Now , DA = AB So , DA² = AB² And , DA² + AC² = AB² + AC² DC² = DA² + AC² BC² = BA² + AC² DC² = BC² So, DC = BC And , Triangles ABC and ADC are congruent AB=AD BC=DC AC=AC (common) ∠CAD =∠CAB = 90° Hop it helps! |
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