Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel. Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram.

Are the opposite sides of a parallelogram always equal?

The opposite sides of a parallelogram are equal. ... The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram bisects it into two congruent triangles. If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.

Does a parallelogram have equal sides Yes or no?

The Parallelogram A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles “A” are the same, and angles “B” are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Are all 4 sides of a parallelogram equal?

Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel. Theorem 1: In a parallelogram, the opposite sides are of equal length. ... Definition 3: A rhombus is a quadrilateral where all four sides have the same length. Theorem 7: A rhombus is a parallelogram.

Do all parallelograms have 4 sides?

Parallelograms are four-sided shapes that have two pairs of parallel sides. Rectangles, squares and rhombuses are all classified as parallelograms. The classic parallelogram looks like a slanted rectangle, but any four-sided figure that has parallel and congruent pairs of sides can be classified as a parallelogram.

Prove: Opposite Sides of Parallelogram are Equal in Length

18 related questions found

Which of the following is not a parallelogram?

Trapezium is not a parallelogram as it has only one pair of parallel sides.

What are adjacent sides of a parallelogram?

Adjacent sides of a parallelogram are equal and one of the diagonals is equal to any one of the sides of this parallelogram. Show that its diagonals are in the ratio square root of 3 :1. A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

What is an opposite side?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. The hypotenuse of a right triangle is always the side opposite the right angle. ...

What are equal adjacent sides?

Definition: Two lines that meet at a polygon vertex. Usually found in triangles and other polygons , two of the sides that meet at a vertex of the polygon are called adjacent sides.

What does a parallelogram have that other quadrilaterals dont?

In word problems, be careful not to assume that a quadrilateral has parallel sides or equal sides unless that is stated. A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. ... No, because a rhombus does not have to have 4 right angles.

Is kite a parallelogram?

Kites are a special type of quadrilateral with two distinct pairs of consecutive sides the same length. ... Similarly, every kite is not a parallelogram, because the opposite sides of a kite are not necessarily parallel. Trapezoids. Trapezoids are quadrilaterals that have one pair of parallel sides.

Which of the following are parallelogram?

Answer: Rectangle, square and rhombus are all parallelograms as in each of these figures, both the pairs of opposite sides are equal and parallel.

How are opposite sides of a parallelogram congruent?

If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other. If a quadrilateral is a parallelogram, then consecutive angles are supplementary.

What do opposite angles in a parallelogram add up to?

The opposite internal angles of a parallelogram are equal and the adjacent angles are supplementary i.e., the sum of the adjacent angles should be equal to 180 degrees. Its diagonals bisect each other..

Are angles of parallelogram always equal?

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of degrees). Since, angles and are opposite interior angles, thus they must be equivalent.

How many sides does a parallelogram have?

A parallelogram has four sides total. The most recognizable parallelogram is the square; however, a parallelogram can be many shapes: A square is the parallelogram that has four equal sides. The opposite sides are parallel and all corners of the square form a right angle.

Which quadrilateral has equal sides?

The only regular (all sides equal and all angles equal) quadrilateral is a square.

Can a trapezoid be a parallelogram?

A trapezoid can be called a parallelogram when it has more than one pair of parallel sides.

Is a trapezoid a square?

A trapezoid is a square if both pairs of its opposite sides are parallel; all its sides are of equal length and at right angles to each other. A trapezoid can be a rectangle if both pairs of its opposite sides are parallel; its opposite sides are of equal length and are at right angles to each other.

Is a diamond a parallelogram?

A parallelogram in which all the edges are of equal length is called a rhombus, or a diamond. In addition to the general properties of parallelograms, in a rhombus, the diagonals bisect the angles, and the diagonals are perpendicular to each other.

Is a parallelogram and four right angles and four equal sides?

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

Has only one pair of opposite sides that are parallel?

A trapezoid is a quadrilateral with one pair of opposite sides parallel. ... Sometimes people define trapezoids to have at least one pair of opposite sides parallel, and sometimes say there is one and only one pair of opposite sides parallel.

Are parallel sides?

Parallel sides are a unique property of certain shapes. These are sides that will never meet and are always the same distance apart. Some shapes that have parallel sides include the parallelogram, the rectangle, the square, the trapezoid, the hexagon, and the octagon.