Question

In a quadrilateral ABCD, O is the mid point of AC,show that the quadrilaterals ABOD and CBOD are equal in area

Answer 1

Answer:

The proof is below.

Step-by-step explanation:

Given In a quadrilateral ABCD, O is the mid point of AC.

we have to prove that the quadrilaterals ABOD and CBOD are equal in area.

In ΔABC,O is the mid-point of side AC

⇒BO is the median of ΔABC

As the median of triangle divides the triangle into two triangle of equal area.

⇒ ar(ABO)=ar(BOC) →  (1)

Also, In ΔADC,O is the mid-point of side AC

⇒DO is the median of ΔADC

As the median of triangle divides the triangle into two triangle of equal area.

⇒ ar(ADO)=ar(DOC) →  (2)

Adding (1) and (2), we get

ar(ABO)+ar(ADO)=ar(BOC)+ar(DOC)

⇒ ar(ABOD)=ar(CBOD)

Hence Proved

Answer 2

Answer:

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Step-by-step explanation:

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