Question

Show that the diagonals of a parallelogram divide in into four triangle of equal area

Answer 1

Answer:

hello...

Given : A parallelogram ABCD With diagonals AC & BD

To prove: ar (AOB) = ar (BOC) = ar (COD) = ar (AOD)

Proof : ABCD is a parallelogram Diagonals of a parallelogram bisect each other :

O is the mid-point of BD, OB = OD . (1)

& O is the mid-point of AC, OA = OC . (2)

In triangle ABC,

Since OA = OC. (From (2)) :

therefore

BO is the median of triangle ABC

= ar(AOB) = ar(BOC) .. (3)

( Median divides the triangle into equal area)

In triangle ADC,

Since OA = OC (From (2)

DO is the median of triangle ADC

= ar(A AOD) = ar(COD) .. .(4)

(Median divides the triangle into equal )

Similarly,

In triangle ABD, Since OB = OD. (From (1)

AO is the median of triangle ABD

ar(AOB) = ar(AOD). (5)

(Median divides the triangle into equal area )

From (3), (4) & (5)

ar (AOB) = ar (BOC) = ar (COD) = ar (AOD) .

Hence proved

I hope it will help you

plz mark as brilliant ans.

Answer 2

Answer: hope it help you please mark as brilliant

Have a great day ☺️