# What is a parallelogram with perpendicular diagonals?

## What is a parallelogram with perpendicular diagonals?

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. To prove a square, you must prove it is both a rectangle and a rhombus.

### Are diagonals perpendicular in a square?

The diagonals of a square intersect (cross) in a 90 degree angle. This means that the diagonals of a square are perpendicular. The diagonals of a square are the same length (congruent).

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

Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square.

**Is a parallelogram with perpendicular diagonals a rhombus?**

A Parallelogram with Perpendicular Diagonals is a Rhombus We’ve seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. Here we will show the converse- that if a parallelogram has perpendicular diagonals, it is a rhombus – all its sides are equal.

**Are diagonals of parallelogram?**

A parallelogram is a quadrilateral whose opposite sides are parallel. The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal. The diagonals of a parallelogram bisect each other.

## Are diagonals of a parallelogram equal?

The diagonals of a parallelogram are equal. The opposite sides and opposite angles of a parallelogram are equal.

### What is the diagonal of a 10×10 square?

Finding the Diagonal of a Square

Square Size | Diagonal |
---|---|

10″ | 14 1/8″ |

10 1/2″ | 14 7/8″ |

11″ | 15 1/2″ |

11 1/2″ | 16 1/4″ |

#### Are diagonals of rhombus equal?

A rhombus has all sides equal, while a rectangle has all angles equal. A rhombus has opposite angles equal, while a rectangle has opposite sides equal. The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.

**What shape is a square but not a parallelogram?**

rhombuses

A rhombus is a quadrilateral (plane figure, closed shape, four sides) with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, but not all rhombuses are squares.

**What shape is always a parallelogram?**

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

## What is the formula of diagonal of parallelogram?

FAQs on Diagonal of Parallelogram Formula For any parallelogram abcd, the formula for the lengths of the diagonals are, p=√x2+y2−2xycosA=√x2+y2+2xycosB p = x 2 + y 2 − 2 x y cos A = x 2 + y 2 + 2 x y cos B and q=√x2+y2+2xycosA=√x2+y2−2xycosB q = x 2 + y 2 + 2 x y cos A = x 2 + y 2 − 2 x y cos

### Is a parallelogram Always Never or sometimes a rectangle?

You have it backwards a rectangle is always a parallelogram, but a parallelogram is not always a rectangle. This is true because parallelogram don’t always have to have all 90 degrees angles while a rectangle always have to.

#### Is a parallelogram always a rectangle?

A rectangle is always a parallelogram, since all four angles are 90 degrees. There is an infinite number of parallelograms with the same side lengths a,b as a rectangle.

**Does square have perpendicular diagonals?**

The diagonals of a square are perpendicular bisectors of one another. As a result, Their intersection forms four right angles, and each diagonal is split into two congruent pieces.

**What do quadrilaterals have diagonals that bisect opposite angles?**

A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus. Opposite angles of a rhombus are equal and diagonals of the Rhombus bisect each other perpendicularly. Note all rhombus are parallelograms but the reverse of this is not true.