Parallelogram ABC

Given.

Parallelogram ABCD of which midpoints are E, F, G and H of sides AB, BC, CD and DA respectively

Formula used.

SAS congruency rule = If 2 sides and angle between them are equal in both triangles then both triangles are congruent

In triangle DGH and triangle BEF

DG= EB AB= CD then their half also be equal

DH= FB BC= DA then their half also be equal

D= B opposite angles of parallelogram are equal

triangle DGH triangle BEF [By SAS congruency]

GH = EF

In triangle AEH and triangle CGF

GC= AE AB= CD then their half also be equal

AH= FC BC= DA then their half also be equal

C= A opposite angles of parallelogram are equal

triangle DGH triangle BEF [By SAS congruency]

HE = GF

If both pair of sides are equal in quadrilateral then this is called parallelogram

EFGH is a parallelogram

Join the mid-points FH

Parallelogram divides in 2 equal parallelograms

In parallelogram ABFH and triangle EFH

Both lies on same base FH

And both lies on parallel lines AB and FH

AB || FH opposite sides of parallelogram are parallel

Then

Area of triangle EFH = × Area of parallelogram ABFH

In parallelogram FHDC and triangle EFG

Both lies on same base FH

And both lies on parallel lines CD and FH

CD || FH opposite sides of parallelogram are parallel

Then

Area of triangle GFH = × Area of parallelogram FHDC

Area of [Δ EFG+Δ GFH]=×Area of parallelogram [ABFH+FHDC]

Area of parallelogram EFGH = ×Area of parallelogram ABCD

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