Question

if the midpoints of the sides of a quadrilateral are joined in order,prove that the area of the parallelogram,so formed will be half the area of the given quadrilateral.

Answer 1

Answer: Proved

Step-by-step explanation:

Given : ABCD is a quadrilateral P,Q,R,S are mid point of the sides AB , BC, CD and AD respectively

To prove : area (PQRS) = 1/2 area( ABCD)

construction : join AC and BD

Proof :  

In the Δ ABD , P and S are the mid point of the sides AB and AD

area (ΔASP) = 1/4 area (ABD)

area (ΔASP) =1/4 × 1/2 area (ABCD)

area (ΔASP) = 1/8 area (ABCD)...(1)

area (ΔBPQ)= 1/8 area(ABCD)..(2)

area (ΔCQR ) = 1/8 area (ABCD) ...(3)

area (ΔRDS ) =1/8 area (ABCD)...(4)

adding all the equation

area (ΔASP +Δ BPQ +ΔCQR +ΔRDS) = 4× 1/8 area( ABCD)

Area (PQRS) = 1/2 area (ABCD )

Answer 2

Answer:

hey mate see attachment

Step-by-step explanation:

mark me as a brainilist