In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Given: Parallelogram ABCD in which E and F are mid - points of AD and BC. To prove: BFDE is a parallelogram Proof: E is the mid-point of AD. DE = AD Also, F is the mid-point of BC. BF = BC But as we know opposite sides of parallelogram are equal. So, AD = BC Therefore, DE = BF And, also AD is parallel to BC. So, DE is parallel to BF. When DE = BF and DE is parallel to BF. (opposite sides are equal and parallel to each other) Hence, BFDE is a parallelogram.

Prove that the diagonals of a parallelogram bisect each other.

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If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

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The given figure shows a parallelogram. The value of x for which it will be a rhombus is :
35°
25°
15°
45°

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A rhombus will be a square, if :
its diagonals bisect each other
its diagonals are perpendicular to each other
one of its angles is 60°
none of these

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Mathematics

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Quadrilaterals

Related Questions

Prove that the diagonals of a parallelogram bisect each other.

If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

The given figure shows a parallelogram. The value of x for which it will be a rhombus is :
35°
25°
15°
45°

A rhombus will be a square, if :
its diagonals bisect each other
its diagonals are perpendicular to each other
one of its angles is 60°
none of these

Mathematics

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Quadrilaterals

Related Questions

Prove that the diagonals of a parallelogram bisect each other.

If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

The given figure shows a parallelogram. The value of x for which it will be a rhombus is :35°25°15°45°

A rhombus will be a square, if :its diagonals bisect each otherits diagonals are perpendicular to each otherone of its angles is 60°none of these

The given figure shows a parallelogram. The value of x for which it will be a rhombus is :
35°
25°
15°
45°

A rhombus will be a square, if :
its diagonals bisect each other
its diagonals are perpendicular to each other
one of its angles is 60°
none of these