Question

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O, at right angles. Prove that AB² + CD² = AD² + BC².

Please tell the correct answer and please tell it fast. I will mark him/her as brainliest
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Answer 1

Answer:

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.