Question

S
Show that the quadrilateral formed by joining the mid-points of
the pairs of adjacent sides of a rhombus is a rectangle.
Hint. Join AC and BD to intersect at O.
Show that PQRS is a ll gm.
Now, EOFR is a Ilgm. So, 2 ERF = _ EOF = 90°)



please friends send me the answer soon ​

Answer 1

Answer:

Margie wrote in her diary, “Today Tommy found a real book”. ... One of the strange things was that after reading the book became useless. Because the text written on it did not change the way it happened on their computer screen.

Answer 2

Consider △ ABC

We know that P and Q are the mid points of AB and BC

By using the midpoint theorem

We know that PQ || AC and PQ = ½ AC

Consider △ ADC

We know that RS || AC and RS = ½ AC

It can be written as PQ || RS and

PR = RS = ½ AC ……. (1)

Consider △ BAD

We know that P and S are the mid points 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)

By considering equations (1) and (2)

The diagonals intersects at right angles in a rhombus

So we get ∠ EQF = 90°

We know that RQ || DB

So we get RE || FO

In the same way SR || AC

So we get FR || OE

So we know that OERF is a parallelogram.

We know that the opposite angles are equal in a parallelogram

So we get

∠ FRE = ∠ EOF = 90°

So we know that PQRS is a parallelogram having ∠ R = 90°

Therefore, it is proved that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rhombus is a rectangle.