Question

How to prove that the quadrilateral formed by joining the midpoints of adjacent sides of a rectangle is a rhombus?

Answer 1

For example using Pythagoras theorem.
Notice that \(DS=SA=BQ=QC\) because this is a rectangle. Analogically \(AP=PB=DR=RC\). Use this and the Pythagoras theorem and you will get \(SP=PQ=QR=RS\), which means that the figure inside is a rhombus.

Answer 2

Thnxx :)