Question

show that the quadrilateral formed by joining the midpoint of the pairs of adjacent sides of a rectangle is a rhombus​

Answer 1

Let is considered ABCD is a quadrilateral with mid point P,Q,R and S respectively.

In  ΔABC, P and Q are mid points of AB and BC respectively.

∴ PQ|| AC and PQ = ½AC ..................(1) (Mid point theorem)

lly in ΔACD, R and S are mid points of sides CD and AD respectively.

∴ SR || AC and SR = ½AC ...............(2) (Mid point theorem)

From equation (1) and (2), we get

PQ || SR and PQ = SR

Hence, PQRS is parallelogram ( opposite sides is parallel and equal)

Therefore, RS || AC and QR || BD.

Also, AC ⊥ BD (Given)

As diagonal bisect each other

∴RS ⊥ QR. 

Thus, PQRS is a rhombus.

Answer 2

Answer:

Step-by-step explanation:

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