Prove that In a parallelogram, opposite side are equal

A quadrilateral is a parallelogram if its opposite sides are equal.

Which of the following is not true for a parallelogram ? a) Opposite sides are equal b) Opposite angles are equal c) Opposite angles are bisected by the diagonals d) Diagonals bisect each other

Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

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

In an isosceles triangle, prove that the angles opposite to equal sides are equal.

A quadrilateral is parallelogram if its opposite angles are equal.

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

Prove that in any parallelogram the sum of squares of the diagonals is twice the sum of the squares of two adjascent sides. Also show that the difference of the squares on two adjacent sides is equal to the rectangle contained by either diagonal and the projection of the other upon it.

Prove that the area of a parallelogram with sides vec(A) and vec(B) " is " vec(A) xx vec(B)