# Which is always true of the diagonals of a parallelogram?

These properties concern its sides, angles, and diagonals. The parallelogram has the following properties: Opposite sides are parallel by definition. The diagonals bisect each other.

The diagonals are congruent. The opposite sides are congruent. The opposite angles are congruent.

Additionally, are the diagonals of a parallelogram equal? When a parallelogram is divided into two triangles we get to see that the angles across the common side( here the diagonal) are equal. This proves that the opposite angles in a parallelogram are also equal. The diagonals of a parallelogram are not of equal length.

Likewise, what is always true of a parallelogram?

By the definition of a parallelogram, we know that the opposite sides are congruent and parallel, so the second and fourth statements are always true. The definition also gives that opposite angles are congruent, so the third statement is always true.

How do you find the diagonals of a parallelogram?

Find the length of diagonal . Explanation: To find the length of the diagonal, we can consider only the triangle and use the law of cosines to find the length of the unknown side. Where is the length of the unknown side, and are the lengths of the known sides, and is the angle between and .

### What property is not true for all parallelograms?

Which property is not true for all parallelograms? 1)Opposite angles are congruent. 2)Consecutive angles are supplementary. 3)Opposite sides are congruent.

### Is a rhombus a parallelogram?

DEFINITION: A rhombus is a parallelogram with four congruent sides. THEOREM: If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles. THEOREM Converse: If a parallelogram has diagonals that bisect a pair of opposite angles, it is a rhombus.

### Is a rectangle a parallelogram?

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.

### Which property is true for all trapezoids?

The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are the same length (congruent). The angles on either side of the bases are the same size/measure (congruent). The diagonals (not show here) are congruent.

### What is not a characteristic of a parallelogram?

If the four sides do not connect at their endpoints, you do not have a closed shape; no parallelogram! If one side is longer than its opposite side, you do not have parallel sides; no parallelogram! If only one set of opposite sides are congruent, you do not have a parallelogram, you have a trapezoid.

### Which quadrilateral always have diagonals that bisect opposite angles?

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If a quadrilateral is a rectangle, then it is a parallelogram. If a parallelogram is a rectangle, then its diagonals are congruent.

### Which statement is always true rhombuses are squares?

Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. This is always true. Squares are quadrilaterals with 4 congruent sides. Since rhombuses are quadrilaterals with 4 congruent sides, squares are by definition also rhombuses.

### Which quadrilateral is a trapezoid?

Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition), making the parallelogram a special type of trapezoid.

### Are diagonals of parallelogram perpendicular?

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

### What are the characteristics of parallelogram?

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. The diagonals bisect each other.

### Are diagonals always perpendicular in a parallelogram?

Problem 1: The opposite sides of a parallelogram are both parallel and congruent. The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.

### What are the different types of parallelograms?

There are three special types of a parallelogram. Rhombus: A parallelogram in which all sides are equal. Rectangle: A parallelogram in which all angles are right angles and the diagonals are equal. Square: A parallelogram with all equal sides and all angles equal to 90 degrees. The diagonals of a square are also equal.

### How do you prove a parallelogram?

To prove a quadrilateral is a parallelogram, you must use one of these five ways. Prove that both pairs of opposite sides are parallel. Prove that both pairs of opposite sides are congruent. Prove that one pair of opposite sides is both congruent and parallel. Prove that the diagonals bisect each other.

Convex polygon