Question

P q R s are respectively mid points of sides ab, BC, CD, da, of a quadrilateral ABCD in which ac=bd and ac is bisector of bd prove that PQRS is a rhombus

Answer 1

Hi

Since , ABCD is a quad. and R,S are the midpoints ,then

RS is parallel to BD and

similarly, QR is parallel to BD

PQ is parallel to RS and

PS is parallel to QR.

that is PQRS is a parallelogram.

Now, AC is perp. to BD.

therefore, ∠1=90°,∠2=90°,∠3=90°,∠4=90°

Hence, PQRS is a rectangle.