Question

A diogonal of a quadrilateral are ABCD are perpendicular to each other . Show. that the quadrilateral formed by joining the mid points of its sides is a rectangle​

Answer 1

Here, ABCD is a quadrilateral. AC and BD are diagonals, which each perpendicular to each other.

P,Q,R and S are the mid-point of AB,BC,CD and AD respectively.

In △ABC,

P and Q are mid points of AB and BC respectively.

∴ PQ∥AC and PQ=

2

1

AC ----- ( 1 ) [ By mid-point theorem ]

Similarly, in △ACD,

R and S are mid-points of sides CD and AD respectively.

∴ SR∥AC and SR=

2

1

AC -----