Question

if the diagonals of a quadrilateral bisect each other then it is a parallelogram

Answer 1

Yes if the diagonals of a quadrilateral bisect each other then it is a parallelogram

Answer 2

If the diagonals of a quadilateral bisect each other,then it is a llgm.

•$\textsf{\underline{\underline{Given:-}}}$

ABCD is a quadilateral.

AO = OC

DO = OB

•$\textsf{\underline{\underline{To\:prove:-}}}$

ABCD is a llgm

i.e, we need to prove that

AB = DC

and AB ll DC

•$\textsf{\underline{\underline{Proof:-}}}$

In ∆AOB and ∆DOC

AO = OC (given)

DO = OB (given)

-- angle 1 = angle 2 (V.O.A)

Therefore, ∆ADB congurent ∆COD (SAS)

AB = DC (cpct) ----- 1.

angle 3 = angle 4 (cpct)

Therefore, AB ll DC ------- 2.

From 1 and 2

Therefore, AB = DC and AB ll DC

Therefore, ABCD is a llgm.