Question

if the diagonals of a quadrilateral are equal and bisect each other at right angle, then quadrilateral is ?

a. rectangle
b. parallelogram
c. rhombus
d. trapezium​

Answer 1

Answer:

ᴛʜᴇ ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴀ ʀʜᴏᴍʙᴜs.

Answer 2

Answer:

c. Rhombus.

Step by Step explanation:

Consider a rhombus ABCD and let its diagonals AC and BD intersect at O

Consider triangle AOB and triangle BOC

In these two triangles,

AB = BC [Sides of a rhombus]

BO = BO [Common Side]

AO = CO [Rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other]

So, triangles AOB and BOC are congruent

So, their corresponding angles and equal

Thus, angle AOB = angle BOC

= x (say)

AOC is a straight line

So, by linear pair property,

angle AOB + angle BOC = 180°

=> x + x = 180° => x = 90°

Thus angle AOB = angle BOC = 90°

It can also be be proved that angle COD = angle AOD = 90° using the same mentioned steps

Thus we get angle AOB = angle BOC = angle COD = angle AOD = 90°

that is, diagonals of a rhombus bisect each other at right angles.

HOPE THIS HELPS...