Question

A quadrilateral with diagonals which:
*bisect each other
*do not intersect at right angles
*are not lines of symmetry

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.

Step-by-step explanation: