Question

prove that the diagonal of rhombus bisects the opposite angle

Answer 1

Proof . – Let ABCD be a rhombus whose diagonal AC and BD intersect at the point O.
We know that the diagonals of a parallelogram bisect each other.
Also we know that every rhombus is a parallelogram.
Therefore OA=OC and OB=OD.
From triangle(COB) and triangle (COD), we have:
CB=CD sides of rhombus.
CO=CO. Common
OB=OD proved
Therefore tri(COB)~tri(COD) by SSS congruence.
=> But Thus, Hence, the diagonals of a rhombus bisect each other at right angles.

Answer 2

diagonals of a rhombus bisect each other at right angles.

Step-by-step explanation:

Proof . – Let ABCD be a rhombus whose diagonal AC and BD intersect at the point O.

We know that the diagonals of a parallelogram bisect each other.

Also we know that every rhombus is a parallelogram.

Therefore OA=OC and OB=OD.

From triangle(COB) and triangle (COD), we have:

CB=CD sides of rhombus.

CO=CO. Common

OB=OD proved

Therefore tri(COB)~tri(COD) by SSS congruence.

=> But Thus, Hence, the diagonals of a rhombus bisect each other at right angles.

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