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Constructions

Question

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

Solution

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Some More Questions From Constructions Chapter

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).

In the given figure, ABED is a parallelogram in which DE = EC. Show that area (ABF) = area (BEC)

In the following figure, ABCD is a parallelogram and EFCD is a rectangle. Also, AL ⊥ DC. Prove that
(i) ar(ABCD) = ar(EFCD)
(ii) ar(ABCD) = DC x AL.

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

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