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Quadrilaterals are four-sided polygons. Although rectangles are the most common quadrilaterals that we see in everyday life, there are many classes of quadrilaterals. The quadrilateral family includes squares, rectangles, rhombuses, parallelograms, kites, and trapezoids, along with other four sided regular and non-regular shapes.

All quadrilaterals have four straight sides, four vertices and four angles. Every quadrilateral has two diagonals. Since a diagonal divides the quadrilateral into two triangles, the sum of angles in a quadrilateral is always 180° + 180° = 360° The chart below shows some special quadrilaterals. Scroll down the page for more examples and solutions of quadrilaterals. Some quadrilaterals do not fit into any of the above listed classifications.

A quadrilateral is a 4-sided polygon.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
&null; Diagonals bisect each other.

A rhombus is a quadrilateral with all 4 sides congruent.
• All the properties of a parallelogram.
• Diagonals are perpendicular.

A rectangle is a quadrilateral with 4 right angles.
• All the properties of a parallelogram.
• Diagonals are congruent.

A square is a rectangle with all 4 sides congruent.
• All the properties of a rhombus and rectangle.

A trapezoid is a quadrilateral with exactly one pair opposite sides parallel. Properties of Quadrilaterals
This video looks at properties of various quadrilaterals.

A quadrilateral is a four-sided polygon (remember that polygon means a simple closed curve with straight edges). There are six named quadrilaterals, and many more which do not have a formal name.
A square is a quadrilateral with congruent sides and angles. Squares are the most regular quadrilateral and have the most properties. A square is also a rectangle, parallelogram, rhombus, kite, and trapezoid.
A rectangle is a quadrilateral with congruent angles. A rectangle is also a parallelogram and a trapezoid. Sometimes a rectangle may also be a square.
A parallelogram is a quadrilateral with two pair of parallel sides. A parallelogram is also a trapezoid. A parallelogram may be a kite, rhombus, or a square.
A trapezoid is the most argued over quadrilateral. Mathematicians and educators have different definitions and even other names. It is called trapezium outside the US. Some define a trapezoid with exactly one pair of parallel sides; others say at least pair.
A rhombus is a quadrilateral with congruent sides. A rhombus may be a square. A rhombus is a kite, a parallelogram and a trapezoid.
A kite is a quadrilateral with two pair of congruent adjacent sides. Opposite sides of kite may or may be parallel.
A lesson on the properties of quadrilaterals (parallelogram, rectangle, square, rhombus, kite, trapezoid).
Properties of Parallelograms:
1) Opposite sides are parallel
2) Opposite sides are congruent
3) Opposite angles are congruent
4) Diagonals bisect each other
5) Any pair of consecutive angles are supplementary

Properties of Kites:
1) Two disjoint pairs of consecutive sides are congruent
2) The diagonals are perpendicular
3) One diagonal is the perpendicular bisector of the other.
4) One of the diagonals bisects a pair of opposite angles
5) One pair of opposite angles are congruent

Properties of Rhombuses:
1) All the properties of a parallelogram.
2) All the properties of a kite
3) All the sides are congruent
4) The diagonals divide the rhombus into four congruent right triangles

Properties of Squares:
1) All the properties of a rectangle and rhombus
2) All diagonals form four isosceles right triangles

Properties of an Isosceles Trapezoid:
1) The legs are congruent
2) The bases are parallel
3) The lower base angles are congruent
4) The upper base angles are congruent
5) The diagonals are congruent
6) Any lower base angle is supplementary to any upper base angle

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