Question

show that quadrilateral formed by joining mid points of a rectangle is a rhombus
​

Answer 1

Answer:

Consider △ ABC We know that P and Q are the midpoints of AB and BC Based on the midpoint theorem We know that PQ || AC and PQ = ½ AC Consider △ ADC Based on the midpoint theorem We know that RS || AC and RS = ½ AC It can be written as PQ || RS and PQ = RS = ½ AC ……. (1) Consider △ BAD We know that P and S are the midpoints of AB and AD Based on the midpoint theorem We know that PS || BD and PS = ½ DB Consider △ BCD We know that RQ || BD and RQ = ½ DB It can be written as PS || RQ and PS = RQ = ½ DB ……… (2) We know that the diagonals of a rectangle are equal It can be written as AC = BD ………. (3) Comparing equations (1), (2) and (3) We know that PQ || RS and PS || RQ So we get PQ = QR = RS = SP Therefore, it is proved that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus