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# What is a parallelogram with congruent and perpendicular diagonals?

## What is a parallelogram with congruent and perpendicular diagonals?

We know a square is a parallelogram with congruent sides and congruent angles, and has diagonals that are congruent and perpendicular.

Which parallelograms have perpendicular bisectors?

Theorem 7: A rhombus is a parallelogram. Theorem 8: A quadrilateral is a rhombus if and only if the diagonals are perpendicular bisectors of each other.

What is a parallelogram in which all sides are congruent?

One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel. If we have a parallelogram where all sides are congruent then we have what is called a rhombus.

### 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.

What is a parallelogram with four congruent sides?

A rhombus is a parallelogram with all four sides congruent to each other. diamond-like shape. A square is a parallelogram with four congruent sides and four right angles. In other words, a square is a rectangle and a rhombus.

Do all parallelograms have 4 equal sides?

A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal.

## Are all Rhombuses parallelograms?

Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite.

Is bisector of parallelogram perpendicular?

All of the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary). The diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.

Do all parallelograms have opposite sides that are perpendicular?

Parallelogram are quadrilaterals with opposite sides parallel, but adjacent sides not perpendicular. If the sides have equal lengths, then it is called a rhombus.

### Is a parallelogram with all four sides congruent?

Do all parallelograms have four congruent sides?

It is a special case of a parallelogram that has four congruent sides and four right angles. A square is also a rectangle because it has two sets of parallel sides and four right angles. A square is also a parallelogram because its opposite sides are parallel. All four sides of a rhombus are congruent.

Does a parallelogram have congruent sides?

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel . Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other.

## When do the sides of a parallelogram become a square?

The diagonals are perpendicular to and bisect each other. A square is a special type of parallelogram whose all angles and sides are equal. Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other. Click to see full answer

How is a rhombus a special type of parallelogram?

It is defined as a quadrilateral all of whose sides are congruent. It is a special type of parallelogram, and its properties (aside from those properties of parallelograms) include: Its diagonals divide the figure into 4 congruent triangles. Its diagonals are perpendicular bisectors of eachother.

Which is characteristic guarantees that a parallelogram is a rectangle?

Answer:- The characteristic guarantees that a parallelogram is a rectangle is “the diagonals are congruent”. The opposite sides are parallel. The opposite sides and angles are equal. The diagonals are perpendicular bisectors.

### Which is the sum of the interior angles of a parallelogram?

The sum of interior angles of a parallelogram is equal to 360°. The consecutive angles of a parallelogram should be supplementary (180°). The 7 important theorems on properties of a parallelogram are given below: A diagonal of a parallelogram divides the parallelogram into two congruent triangles.