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ABCD is a quadrilateral in which P,Q,R and S midpoint of the sides AB,BC,CD and DA respectively.If BD=12 cm Then the length of QR Is |
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Answer» Answer: In the TRIANGLE, ΔACD, S and R are MIDPOINTS of AD and CD. So, from Midpoint theorem, we can say that, SR∣∣AC and SR=12AC->(1) Similarly, in the triangle, ΔACB, P and Q are midpoints of AB and CB. So, from Midpoint theorem, we can say that, PQ∣∣AC and PQ=12AC->(2) From (1) and (2), SR=PQ=12AC Also, as both SR and PQ are parallel to AC, so, both of them should also be parallel to each other. So, PQ=SRandPQ∣∣SR Similarly, we can show that , SP∣∣RQandSP=RQ Thus, PQRS is a parallelogram. There goes your answer. PLEASE mark me as branlist |
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