# Can parallelogram be a rectangle?

## Can parallelogram be a rectangle?

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram, plus the following: The diagonals are congruent.

## Is a parallelogram is always a rectangle?

Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. A parallelogram is a rectangle. This is sometimes true.

## Under what circumstances is a parallelogram a rectangle?

Name That Quadrilateral,? your answer must be as general as possible. Because a square is a rectangle but a rectangle need not be a square, the most general quadrilateral that fits this description is a rectangle. Theorem 16.5: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

## Why is a parallelogram not rectangle?

A parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides. A rectangle is a quadrilateral with 2 pairs of opposite, equal and parallel sides BUT ALSO forms right angles between adjacent sides. This is not true for all parallelograms since isn’t necessary that any of the angles is 90°.

## What are the two methods to prove a parallelogram is a rectangle?

1) Show that all angles are 90 degrees. 2) Show that one set of sides is parallel ,and that two opposite angles are 90 degrees. 3) Show that the diagonals bisect each other, and that they are equal in length. 4) Show that it is a parallelogram and that diagonals are equal in length.

## How do you prove a rectangle is a parallelogram?

If the diagonals of a parallelogram are congruent, then it’s a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it’s a rectangle (neither the reverse of the definition nor the converse of a property).

## How do you change a parallelogram into a rectangle?

In this parallelogram, you can cut the triangle from the left of the parallelogram and move it to the right side of the parallelogram, making a rectangle. We know the formula for finding the rectangle’s area is base • height, so the area of this shape is 8 • 5, which is 40 square units.

## Which explains whether or not a parallelogram can be classified as a rectangle?

A rectangle is considered a special case of a parallelogram because: A parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides. The same way that not all rectangles are squares, not all parallelograms are rectangles. A rectangle is a parallelogram with 4 right angles.

## How do you prove that a rectangle is a parallelogram?

All rectangles are parallelograms. If a parallelogram has (at least) one right angle, then it is a rectangle. If a quadrilateral has 2 pairs of opposite sides that are congruent, then it is a parallelogram. If the diagonals of a quadrilateral both bisect each other, then the quadrilateral is a parallelogram.

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

Therefore, the strongest statement we can use to prove that a parallelogram is a rectangle is: The diagonals of the parallelogram are congruent.

## Why is the area of a parallelogram not the same as a rectangle?

Because the parallelogram and rectangle are composed of the same parts, they necessarily have the same area. Because base × height gives the area of the rectangle, we can use the same measurements on the parallelogram to compute its area: base × height.

## When is a quadrilateral equal to a parallelogram?

A quadrilateral is a parallelogram if its opposite angles are equal. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A quadrilateral is a parallelogram, if its one pair of opposite sides is equal and parallel.

## What is the similarity between a rectangle and a parallelogram?

Rectangle Classification. These are both quadrilaterals, with a rectangle being classified as a type of parallelogram. Angles. The opposite internal angles of both a parallelogram and rectangle are equivalent. Diagonals. In the case of a parallelogram, the diagonals are unequal, and it bisects the shape into two congruent triangles. Formulas.

## How does a parallelogram relate to a rectangle?

Rectangles are special species of the parallelogram. Like a parallelogram, rectangles also have equal and parallel opposite sides. They have equal opposite internal angles and have adjacent angles as supplementary. Rectangles are differentiated from parallelograms because all the internal angles of a rectangle are equal to 90 degrees.

## When can a parallelogram also be called a square?

The only parallelogram that satisfies that description is a square. Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square. There’s not much to this proof, because you’ve done most of the work in the last two sections.