# A quadrilateral having both diagonals congruent is a?

If both pairs of opposite sides are parallel: A Rectangle, or a Square.

If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid.

If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite

It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral

### If one side of a quadrilateral is congruent to its opposite side then the quadrilateral is a parallelogram?

No, it doesn't have to be. A quadrilateral can definitely be a parallelogram only if: - Both pairs of opposite sides are parallel. - Both pairs of opposite sides are congruent. - One pair of opposite sides are both congruent and parallel. - Both pairs of opposite angles are congruent. - The diagonals bisect each other.

### Conditions which guarantee that a quadrilateral is a parallelogram?

Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

### What are the proofs that a quadrilateral ia s parallelogram?

There are 5 ways to prove a Quadrilateral is a Parallelogram. -Prove both pairs of opposite sides congruent -Prove both pairs of opposite sides parallel -Prove one pair of opposite sides both congruent and parallel -Prove both pairs of opposite angles are congruent -Prove that the diagonals bisect each other

### What is a description of a parallelogram?

A parallelogram is a quadrilateral (4-sided figure) with both pairs of opposite sides parallel. That's usually the primary definition. There are properties common to all parallelograms: opposite sides are congruent, opposite angles are congruent, and diagonals bisect each other. Other special parallelograms have additional properties. A rectangle is a parallelogram with four right angles and its diagonals are congruent. A rhombus is a parallelogram with four congruent sides. Its diagonals are perpendicular and each diagonal…

### What is true of all parallelograms?

The definition of a parallelogram is that it's a quadrilateral in which both pairs of opposite sides are parallel. So, that part is true about all parallelograms. Apart from that, there are some other properties that can be deduced, such as: * Opposite sides are congruent * Opposite angles are congruent * The diagonals bisect one another * The sum of the squares of the sides equal the sum of the squares of the diagonals…

### Are all quadrilaterals parallelograms-?

Answer: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. If a quadrilateral is a parallelogram, the 2 pairs of opposite sides are congruent. If a quadrilateral is a parallelogram, the 2 pairs of opposite angles are congruent. Answer: No. On the other hand, all parallelograms are quadrilaterals.

### What shape has diagonals that are perpendicular?

The diagonals of a rhombus are perpendicular. A rhombus is a special kind of parallelogram. It has the characteristics of a parallelogram (both pairs of opposite sides parallel, opposite sides are congruent, opposite angles are congruent, diagonals bisect each other.) It also has special characteristics. It has four congruent sides. So it looks like a lopsided or squished square. Its diagonals are perpendicular. Another property: each diagonal bisects two angles of the rhombus.