Question

if the diagonals of a parallelogram intersect at right angles,prove that it is a rhombus.​

Answer 1

Answer:

easy

Step-by-step explanation:

if in a parallelogram the diagonals intersect at 90 degrees it will be a rhombus

conditions for any quadrilateral to be rhombus are

1)a quadrilateral with all sides equal is a rhombus

2)a parallelogram with any pair of adjacent sides equal is a rhombus

3)a parallelogram whose diagonals intersect at 90 degrees is a rhombus

Answer 2

Answer:

Given: ABCD is a quadrilateral. AC and BD intersect at right angles. P, Q, R, S are mid points of respective sides......✔✔

In

△ABC,

PQ∥AC

and

PQ=2/1 AC

(By mid point theorem).....✔✔

In

△ADC,

SR∥AC

, and

SR=2/1AC

(By mid point theorem).....✔✔

Therefore,

PQ=SR

and

PQ∥SR

Similarly,

PS=RQ

and

PS∥RQ

hence, PQRS is a parallelogram......✔✔

Since,

PQ∥AC

and

QR∥BD

But,

AC⊥BD

Hence,

PQ⊥QR

(Angles between two lines = Angles between their parallels).....✔✔

Thus,

PQRS is a rectangle.....✔✔