Question

the diagonal of a rohmbus bisect each other ______ angels​

Answer 1

LetABCD 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.

ThereforeOA=OC and OB=OD.

FromΔ(COB) and Δ(COD), we have:

CB=CD .....sides of rhombus

CO=CO ....Common side

OB=OD Hence, proved

Therefore Δ(COB) Δ(COD) by SSS congruence.

∠COB=∠COD

But ∠COB+∠COD=180

Thus, ∠COB=∠COD=90

Hence, the diagonals of a rhombus bisect each other at right angles