# Free CBSE Class 9 Maths Areas of Parallelograms and Triangles Worksheets

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## Sample CBSE Class 9 Maths Areas of Parallelograms and Triangles Worksheet Questions

1.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

2.

ABCD is a trapezium with AB $\parallel$ DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).

3.

Diagonals AC and BD of a trapezium ABCD with AB$\parallel$DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

4.

. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that
ar($\bigtriangleup&space;ABE$) = ar($\bigtriangleup&space;ACF$)

5.

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

6.

In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC).

7.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(APB) = ar(BQC).

8.

If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that
ar (EFGH) = 1/2 ar(ABCD).

9.

In triangle PQR, S and T are points on PQ and PR respectively. If ar (QSR) = ar (QTR). Show that $\angle&space;OST&space;=&space;\angle&space;ORQ$

10.

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle?

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