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Constructions
Question
Wired Faculty App

D and E are points on sides AB and AC respectively of ΔABC such that ar(ΔDBC) = ar(ΔEBC). Prove that DE || BC.

Answer

Given: D and E are points on sides AB and AC respectively of ΔABC such that ar(ΔDBC) = ar(ΔEBC).

To Prove: DE || BC.
Proof: ∵ ΔDBC and ΔEBC are on the same base BC and have equal areas.
Their altitudes must be the same.
∴ DE || BC.

Sponsor Area

Some More Questions From Constructions Chapter

Prove that of all parallelograms of which the sides are given, the parallelogram which is a rectangle, has the greatest area.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

Parallelograms on the same base and between same parallels are equal in area. Prove this.

ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

In the given figure, AB | | DC. Show that ar(BDE) = ar(ACED).