How do you prove PQRS is a parallelogram?

How do you prove 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. We can compute the slopes of lines QR and PS to find that both slopes are equal to \frac{y_4 – y_2}{x_4 – x_2}.

How do you conclude a parallelogram?

If a quadrilateral is a parallelogram, then two pairs of opposite angles are congruent. If a quadrilateral is a parallelogram, then two pairs of consecutive angles are supplementary. If a quadrilateral is a parallelogram, then diagonals bisect each other.

What can you conclude about the sides of a parallelogram?

In the above investigation, we drew a parallelogram. From this investigation we can conclude: Opposite Sides Theorem: If a quadrilateral is a parallelogram, then the opposite sides are congruent. Opposite Angles Theorem: If a quadrilateral is a parallelogram, then the opposite angles are congruent.

What conditions makes quadrilateral PQRS a parallelogram?

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. In the quadrilateral PQRS, PQ ≅ RS and PS ≅ QR. Therefore, PQRS is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Are parallelograms Pqrs rhombus?

S P R Q Since the parallelogram is a rhombus and a rectangle, it is a square. Diagonals are perpendicular, so PQRS is a rhombus.

Is parallelogram PQRS a square?

In the given figure PQRS is a parallelogram in which PQ ∥ SR and PS ∥ QR. Rectangle: A parallelogram is called a rectangle if one of its angle is a right angle. In the given figure, PQ = QR = RS = SP and ∠SPQ = ∠PQR = ∠QRS = ∠RSP = 90°. So, PQRS is a square.

How do you conclude that the 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).

Does a SSS congruence relationship exist for parallelograms?

SSSS does not exist as a method to prove that parallelograms are congruent. If you see this common error…, it might mean this… Students trying to show adjacent sides are perpendicular… They are only looking at special quadrilaterals.

What are the rules for a parallelogram?

Properties of Parallelograms Explained

• 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.

What can you conclude about the sides angles and diagonals of a parallelogram?

Opposite sides of a parallelogram are equal. Opposite angles of a parallelogram are equal. Diagonals of a parallelogram bisect each other. If one pair of opposite sides is equal and parallel in a quadrilateral then it is a parallelogram.

Can a quadrilateral PQRS be a parallelogram?

Yes, it can parallelogram. As we know that opposite sides of parallelogram is equal and sum of its adjacent angles be 180 degrees.

The word quadrilateral means the four sides, quad means four, and laterals mean sides, therefore, quadrilateral has four sides. The name of the four sides of the PQRS are: PQ, QR, RS, and SP are the four sides of the quadrilateral. So, there are two diagonals of the quadrilateral named PR and QS.

What are the rules of a parallelogram?

A parallelogram is a quadrilateral made from two pairs of intersecting parallel lines. There are several rules involving: the angles of a parallelogram. the sides of a parallelogram. the diagonals of a parallelogram. Rule 1: Opposite sides are parallel Read more. Rule 2: Opposite Sides are Congruent Read more.

What are the properties of a parallelogram?

Properties, Shapes, and Diagonals. A parallelogram is a quadrilateral made from two pairs of intersecting parallel lines. There are several rules involving: the angles of a parallelogram. the sides of a parallelogram.

When is a quadrilateral a parallelogram?

Quadrilateral CDEF is a parallelogram when x = 4. TTheoremsheorems Theorem 7.9 Opposite Sides Parallel and Congruent Theorem If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. If BC — AD — and BC — ≅ AD —, then ABCD is a parallelogram. Proof Ex. 40, p. 383

What is the theorem for the construction of a parallelogram?

Parallelogram Diagonals Theorem (Theorem 7.6) and Parallelogram Diagonals Converse (Theorem 7.10) 28. CONSTRUCTION Describe a method that uses the Opposite Sides Parallel and Congruent Theorem (Theorem 7.9) to construct a parallelogram. Then construct a parallelogram using your method. 29.