A) PQRS is a rectangle
B) PQRS is a parallelogram
C) Diagonals of PQRS are equal
D) Diagonals of PQRS are at right angles
Correct Answer: D
Solution :
Let A, B, C and D be the mid-points of PQ, QR, RS and SP respectively Now, In \[\Delta RSQ,C\]and B are the mid-points of RS and RQ respectively. So, by mid-point theorem. \[CB||SQ\] ?(i) Similarly, In \[\Delta PSQ,\] \[DA||SQ\] ?(ii) In \[\Delta SPR,\] \[CD||RP\] ?(iii) Also, in\[\Delta QRP\] \[AB||RP\] ?(iv) From (i) and (ii), \[CB||DA\] ?(v) From (iii)and (iv), \[CD||AB\] Hence, from (v) and (vi), ABCD is a parallelogram. Now, if diagonals bisect SQ and PR are at \[{{90}^{o}}\] Then, \[CB\bot CD,\,CB\bot AB,\,AB\bot DA\]and \[AD\bot CD.\] So, ABCD is a rectangle.You need to login to perform this action.
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