Question

in rhombus ABCD AB=BC=CD=DA how?​

Answer 1

Answer:

ANSWER

According to the given statement, the figure will be a shown alongside; using mid-point theorem:

In △ABC,PQ∥AC and PQ=

2

1

AC .......(1)

In △ADC,SR∥AC and SR=

2

1

AC .......(2)

∴PQ=SR and PQ∥SR from (1) and (2)

⇒PQRS is a parallelogram.

Now,PQRS will be a rectangle if any angle of the parallelogram PQRS is 90

∘

PQ∥AC(by midpoint theorem)

QR=BD(by midpoint theorem)

But AC⊥BD(diagonals of a rhombus are perpendicular to each other)

∴PQ⊥QR(angle between two lines = angle between their parallels)

Hence PQRS is a rectangle.

Answer 2

Because rhombus is a parallelogram with equal sides.

Properties of a Rhombus

(1) All the properties of a parallelogram.

(2) Diagonals are perpendicular to each other