Table of Contents

## Can a quadrilateral ABCD be?

It can be, but here it needs not to be. Since opposite angles are equal in parallelogram and here opposite angles are not equal in quadrilateral ABCD.

**Can a quadrilateral be a parallelogram if?**

There are five ways in which you can prove that a quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

**Is the quadrilateral ABCD a parallelogram?**

Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D . We know that the sum of the angles of a quadrilateral is 360o. Hence, ABCD is a parallelogram.

### Which of the following condition can make the quadrilateral ABCD a parallelogram?

If you have a quadrilateral that has diagonals that bisect each other, your quadrilateral is a parallelogram. Figure 16.4 shows a parallelogram ABCD with diagonals AC and BD that intersect at M and bisect each other.

**Is ABCD a parallelogram Why?**

The shape of quadrilateral ABCD changes as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCD is a parallelogram by the Parallelogram Opposite Sides Converse. By the definition of a parallelogram, — AB — DC .

**Is quadrilateral ABCD a parallelogram if a 70?**

No, the quadrilateral ABCD is not a quadrilateral because in a parallelogram the opposite angles are equal and if that is true then angles are 70, 65, 70, 65 which is not possible as their sum is not 360 also sum of consecutive angels must be 180.

## What are the conditions that guarantee a quadrilateral is a parallelogram?

Well, we must show one of the six basic properties of parallelograms to be true!

- Both pairs of opposite sides are parallel.
- Both pairs of opposite sides are congruent.
- Both pairs of opposite angles are congruent.
- Diagonals bisect each other.
- One angle is supplementary to both consecutive angles (same-side interior)

**Can a quadrilateral ABCD be a parallelogram if 70 and C 65?**

**How do you prove a quadrilateral?**

Here are the six ways to prove a quadrilateral is a parallelogram:

- Prove that opposite sides are congruent.
- Prove that opposite angles are congruent.
- Prove that opposite sides are parallel.
- Prove that consecutive angles are supplementary (adding to 180°)
- Prove that an angle is supplementary to both its consecutive angles.

### Which quadrilateral is a parallelogram?

A rectangle is a quadrilateral in which all angles are right angles. A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.

**Is a quadrilateral a parallelogram yes or no?**

Yes. A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rectangle are parallel, so every rectangle is a parallelogram.

**Is a rhombus a parallelogram?**

Every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. A rhombus with right angles is a square….

Rhombus | |
---|---|

Type | quadrilateral, trapeziod, parallelogram, kite |

Edges and vertices | 4 |

Schläfli symbol | { } + { } {2α} |

Coxeter diagram |