Answer :

Given.

ABCD is a parallelogram and ABCE is a quadrilateral

Diagonal AC divides the quadrilateral shaped region ABCE into two equal parts

Formula used.

If 2 triangles are on same base And having equal area then they lies between 2 parallel lines.

Diagonal of parallelogram divide it into 2 congruent triangles

In quadrilateral ABCE

As AC divides quadrilateral into 2 equal parts

Triangle ABC = triangle AEC

In parallelogram ABCD

As AC is diagonal which divides parallelogram into 2 equal triangles

Triangle ABC = triangle ADC

Comparing both

We get

Triangle AEC = triangle ADC

As both triangles triangle AEC ,Δ ADC are equal

And both lies on same base AC

Hence both triangles comes between parallel lines AC , DE

∴ AC || DE

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