Question

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

Solution

Given: ABCD is a parallelogram in which DE = EC To Prove: area (ABF) = area (BEC)
Proof: AB = DE
| Opposite sides of a parallelogram DE = EC | Given
∴ AB = EC Also, AB || DE
| Opposite sides of a parallelogram ⇒ AB || DC
Now, ΔABF and ΔBEC are on equal bases AB and EC and between the same parallels AB and DC
∴ ar(ΔABF) = ar(ΔBEC)

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.

For Daily Free Study Material Join wiredfaculty

Constructions

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

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Constructions

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

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.