Question

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Answer 1

Answer:

The diagonals of a parallelogram divide it into four triangles of equal

Step-by-step explanation:

Let say ABCD is a parallelogram

Diagonals intesecting at O

now in Δ AOD   & Δ BOC

AD = BC  (opposite sides are equal of paralleogram)

∠ADO = ∠CBO   as AD ║ BC  (opposite sides are parallel in Parallelogram) , also

∠DAO = ∠BCO

=> Δ AOD   ≅ Δ BOC

=> OA = OC   & OB = OD

Δ AOD   ≅ Δ BOC

=> Area of  Δ AOD  = Area of Δ BOC

Similarly Area of  Δ AOB  = Area of Δ DOC

in Δ ABD

OB = OD = BD/2

=> AO is median of Δ ABD

Median divides Triangle into two equal area triangles

=> Area of Δ AOD = area of Δ AOB

Area of  Δ AOD  = Area of Δ BOC

Area of  Δ AOB  = Area of Δ DOC

Area of Δ AOD = area of Δ AOB

=> Area of  Δ AOD = Area of Δ BOC = area of Δ AOB = Area of Δ DOC

=> The diagonals of a parallelogram divide it into four triangles of equal area.