ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove

that: (1) ar (ΔADO) = ar (ΔCDO) (2) ar (ΔABP) = ar (ΔCBP)

Advertisement Remove all ads

#### Solution

Given that ABCD is a parallelogram

To prove: (1) ar (ΔADO) = ar (ΔCDO)

(2) ar ( ΔABP) = ar (ΔCBP)

Proof: We know that, diagonals of a parallelogram bisect each other

∴ AO = OC and BO = OD

(1) In ΔDAC , since DO is a median

Then area (ΔADO) = area (ΔCDO)

Then area (ΔADO) = area (ΔCDO)

(2) In ΔBAC , Since BO is a median

Then; area (ΔBAO) area (ΔBCO) ......(1)

In a ΔPAC, Since PO is a median

Then, area (ΔPAO) = area (ΔPCO) ......(2)

Then; area (ΔBAO) area (ΔBCO) ......(1)

In a ΔPAC, Since PO is a median

Then, area (ΔPAO) = area (ΔPCO) ......(2)

Subtract equation (2) from equation (1)

⇒ area (ΔBAO) - ar (ΔPAO) ar (ΔBCO) - area (ΔPCO)

⇒ Area (ΔABP) = Area of ΔCBP

⇒ Area (ΔABP) = Area of ΔCBP

Concept: Concept of Area

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads