Question

what type of quadrilateral is it, whose diagonals does not intersect?​

Answer 1

Given: ABCD is a quadrilateral. AC and BD intersect at right angles. P, Q, R, S are mid points of respective sides.

In △ABC,

PQ∥AC and PQ=

2

1

AC (By mid point theorem)

In △ADC,

SR∥AC, and SR=

2

1

AC (By mid point theorem)

Therefore, PQ=SR and PQ∥SR

Similarly, PS=RQ and PS∥RQ

hence, PQRS is a parallelogram.

Since, PQ∥AC and QR∥BD

But, AC⊥BD

Hence, PQ⊥QR (Angles between two lines = Angles between their parallels)

Thus, PQRS is a rectangle.

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