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Prove that digonals of a rectangle are equal |
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Answer» Since rectangles have right angles in each corner and opposite sides of a rectangle are CONGRUENT, then in rectangle ABCD it would be TRUE that AB is congruent to CD. Therefore by the Pythagorean Theorem: AB² + BC² = AC² and CD² + BC² = BD² But since AB = CD, it follows that AB² = CD² so AB² + BC² = CD² + BC² which simplifies to AC² = BD² If AC² = BD² then AC = BD, proving diagonals are of equal LENGTH. I hope that helps. |
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