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Answer 1

Answer:

1. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel . A parallelogram also has the following properties: ... Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other.

2. a parallelogram in which at least two consecutive sides are equal in length. ... a quadrilateral with four sides of equal length (by definition) a quadrilateral in which the diagonals are perpendicular and bisect each other. a quadrilateral in which each diagonal bisects two opposite interior angles.

3. The Rectangle is the ideal definition of a Parallelogram with its parallel opposite sides of equal length. Opposite sides are congruent and all corners form congruent 90 degree angles. ... The sum of angles of a Parallelogram equals 360 degrees.

Step-by-step explanation:

Hope it will help you!!!

Answer 2

Step-by-step explanation:

In the above quadrilateral, one pair of opposite sides AB // DC. And any one pair of opposite angles < A = <C

In these given conditions the quadrilateral has to be a parallelogram.

Proof: since angle A = angle C (given )

And DC // AB ( given)

=> angle DCB = angle CBE ( alternate interior angles formed by parallel lines) …..(1)

But angle DCB = angle DAB ( given)……(2)

=> angle DAB = angle CBE ( by (1) & (2)

=> AD // BC ( as consecutive interior angles are equal)

This way, both the pairs of opposite sides become parallel. So, it's a parallelogram.