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ABCD is a parallelogram, if the two diagonalsareequal. Find the measure of LABC , |
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Answer» Answer: Since ABCD is a PARALLELOGRAM. THEREFORE, AB=CD and AD=BC Thus, in △ABD and △ ACB, AD=BC BD=AC AB=AB So, by SSS CRITERION of congruence, △ABD≅△ACB Therefore, ∠BAD=∠ABC Now, AD∥BC and transversal AB INTERSECTS them at A and B respectively. Therefore, ∠BAD+∠ABC=180 o
∠ABC+∠ABC=180 o
2∠ABC=180 o
∠ABC=90 o
Hence, the measure of ∠ABC is 90 |
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