Question

prove that diagonals of a Rhombus bisect each other at right angles As given in the adjoining figure​

Answer 1

Given

• A rhombus Abcd
• In which Diagonal AC and BD passes to each other

To Proof

• Diagonal Bisect each other
• And cut at 90°

Proof

In∆ABO & OCD

CD =AB (All side equal side)

BDC=ABD (AB// CD)

DOC=AOB

$\sf\red\triangle\:ABO\cong\:\triangle\:OCD$

$\begin{cases} AO=OC\\BO=OD\end{cases}$By cpct

Similarly

By taking AOD & AOB

Both are congruent

By cpct

AoD=AoB

Now taking sum of both angle

2AoD=180°

AoD=90=AoB