What theorems prove a quadrilateral is a parallelogram?. In this article we will let you know details of your question. Also we will share with most asked related question by peoples end of this article. Let's check it out!

## What theorems prove a quadrilateral is a parallelogram?

Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

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## How do you prove a quadrilateral is a parallelogram proof?

1. Prove that both pairs of opposite sides are parallel.
2. Prove that both pairs of opposite sides are congruent.
3. Prove that one pair of opposite sides is both congruent and parallel.
4. Prove that the diagonals bisect each other.

## What does Theorem 5 use to prove a quadrilateral is a parallelogram?

Theorem 5-6 If both pair of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 5-7 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

## What are the theorems to prove a parallelogram?

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

## What are the 6 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.

## What makes a parallelogram a parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle. … The polygon diagonals of a parallelogram bisect each other (Casey 1888, p. 2). Original article published on whoatwherewhy.com

## When a quadrilateral is a parallelogram?

A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure.

All parallelograms are quadrilaterals, so if it is a parallelogram, it is also a quadrilateral. The correct answer is that all trapezoids are quadrilaterals.

### How many theorems are there in parallelogram?

Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

### What theorem can you use to show that the quadrilateral is a parallelogram see top of page?

Parallel Congruent Sides Theorem: If a quadrilateral has one set of parallel lines that are also congruent, then it is a parallelogram.

### Which of the following conditions guarantee 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.

### Which statements prove that a quadrilateral is a parallelogram quizlet?

if one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

### Which quadrilateral is not a parallelogram?

A trapezium is the quadrilateral that is not a parallelogram as its two sides are not parallel.

### Is parallelogram a cyclic quadrilateral?

Parallelogram: Any parallelogram cannot be cyclic because if any quadrilateral is cyclic, then the sum of the opposite angles must be 180°. But in the case of a parallelogram, the opposite sides are equal, not supplementary. Therefore, it cannot be a cyclic quadrilateral.

Lesson Summary All rectangles are cyclic, but many other quadrilaterals are not. In a cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees. If a quadrilateral has one pair of opposite angles that add to 180, then you know it is cyclic.. This article is first published on whoatwherewhy.com

### What is the cyclic quadrilateral theorem?

The ratio between the diagonals and the sides can be defined and is known as Cyclic quadrilateral theorem. If there’s a quadrilateral which is inscribed in a circle, then the product of the diagonals is equal to the sum of the product of its two pairs of opposite sides.

There are many different types of quadrilaterals and they all share the similarity of of having four sides, two diagonals and the sum of their interior angles is 360 degrees. They all have relationships to one another, but they are not all exactly alike and have different properties.

### Are quadrilaterals and parallelogram quite the same How?

The difference between parallelogram and quadrilateral is that a parallelogram is a four-sided shape which has its opposite sides having an equal length to each other, and on the other hand, the quadrilateral is a four-sided shape that may or may not have its opposite sides equal to each other as such like the …

### Why are some quadrilaterals not parallelograms?

Explanation: An ordinary quadrilateral with no equal sides is not a parallelogram. A kite has no parallel lines at all. A trapezium and and an isosceles trapezium have one pair of opposite sides parallel.

### What properties of parallelograms can be used to prove parallelogram theorems select all that apply?

• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

### What are the 7 properties of a parallelogram?

• Opposite sides are parallel. …
• Opposite sides are congruent. …
• Opposite angles are congruent. …
• Same-Side interior angles (consecutive angles) are supplementary. …
• Each diagonal of a parallelogram separates it into two congruent triangles. …
• The diagonals of a parallelogram bisect each other.

### How do you prove a quadrilateral is a parallelogram if the diagonals bisect each other?

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

### Which answer correctly describes how do you prove quadrilateral QRST is a parallelogram?

which answer correctly describes how to prove quadrilateral qrst is a parallelogram? show that ∠tqs≅∠rst by the alternate interior angles theorem. … since qt∥rs, qr≅st and qt≅rs, so qrst is a parallelogram by definition.

### Which of the following conditions did not guarantee that a quadrilateral is a parallelogram?

The description that does not guarantee that a quadrilateral is a parallelogram is d. quadrilateral with 2 opposite sides parallel. The definition of a parallelogram is a quadrilateral with both pairs of opposite sides that are congruent, their diagonals bisect each other and the consecutive angles are supplementary.

### What statement proves that PQRS is a parallelogram?

To prove that PQRS is a parallelogram, we will check that side PQ is parallel to SR and that QR is parallel to PS. These slopes are the same; therefore, the lines PQ and SR are parallel.

### Which statement can be used to prove that a given parallelogram is a rectangle quizlet?

If a parallelogram contains at least one right angle, then it is a rectangle (definition). 2. If the diagonals of a parallelogram are congruent, then it is a rectangle.

### Which statement proves that WXYZ is a parallelogram?

ANSWER: Yes; the midpoint of . By the definition of midpoint, . Because the diagonals bisect each other, WXYZ is a parallelogram.