# What are the 5 ways to prove a quadrilateral is a parallelogram?

## What are the 5 ways to prove a quadrilateral is a parallelogram?

Criteria proving a quadrilateral is parallelogram 1) If a quadrilateral has one pair of sides that are both parallel and congruent. 2) If all opposite sides of the quadrilateral are congruent. 3) Both pairs of opposite sides are parallel. 4) Opposite angles are congruent.

### How do you prove that a given quadrilateral is a parallelogram?

If both pairs of opposite sides of a quadrilateral are parallel, then it’s a parallelogram (reverse of the definition). If both pairs of opposite sides of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).

#### How do you prove a quadrilateral is a trapezoid?

To prove that it is a trapezoid, remember that the definition of a trapezoid is a quadrilateral with exactly one pair of parallel sides. Therefore, to prove it is a trapezoid you must verify that one pair of sides is parallel. From algebra, remember that two lines are parallel if they have the same slope.

How do you prove a quadrilateral is a rectangle?

There are a few ways to prove a quadrilateral is a rectangle. Here are three of the easiest ways: 1) Show all angles are 90°; 2) Show that one pair of sides is parallel and that two opposite angles are 90°; 3) Show the diagonals bisect each other and are of equal length.

How do you prove a quadrilateral is a rhombus?

To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of opposite angles.

## How do you prove a quadrilateral is a square?

Proving that a Quadrilateral is a Square If the quadrilateral is a rectangle with two consecutive sides congruent, then it is a square. If the quadrilateral is a rectangle with perpendicular diagonals, then it is a square. If the quadrilateral is a rhombus one of whose angles is a right angle, then it is a square.

### How do you prove a quadrilateral is a kite?

How to Prove that a Quadrilateral Is a Kite

1. If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it’s a kite (reverse of the kite definition).
2. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, then it’s a kite (converse of a property).

#### Is a quadrilateral always a rectangle?

A rectangle, by definition, is a polygon with four sides and four right angles. Every rectangle is a quadrilateral because all rectangles must have four sides, which is the definition of a quadrilateral.

Is a quadrilateral a rectangle yes or no?

Yes. A rectangle is a quadrilateral with 4 right angles. Every square has 4 right angles, so every square is a rectangle.

Is a quadrilateral always a parallelogram? Explanation: A Quadrilateral is only a 4 sided figure & has no specific features, whereas a Parallelogram is a 4 sided figure with opposite sides parallel and equal, opposite angles equal and adjacent angles in a linear pair. A Quadrilateral is not a Parallelogram.

## How do you make a quadrilateral?

Constructing quadrilaterals can be done through 4 ways. 1) When 4 sides and one diagonal are given. Construct the quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.5 cm, AD= 5 cm and AC = 8 cm. Step 2: With 4 cm as radius from A draw an arc. Step 3: With 6 cm as radius cut the arc drawn in step 2.