November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Special Quadrilaterals.

This mini-lesson is on special types of quadrilaterals. So far the focus of learning was on properties of quadrilaterals. Now you'll explore, with the help of some examples and solution, how these properties and knowledge will be used for special quadrilaterals- a parallelogram, rectangle, square, rhombus, trapezoid, an isosceles trapezoid and kites.

A parallelogram is a quadrilateral, if both pairs of opposite sides are equal and parallel to each other. Also in case of parallelogram, opposite sides and opposite angles are congruent and diagonals bisect each other.

A rectangle is a parallelogram with four right angles. Opposite sides of a rectangle are parallel and equal. The diagonals of a rectangle are congruent. A square is rectangle with four congruent sides. Opposite sides of a square are parallel and all sides are equal in length and all angles are equal to 90°.

A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel and opposite angles are equal. The diagonals of a rhombus are perpendicular and bisect each other.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is a quadrilateral where two opposite sides are parallel, the two other sides are of equal length. Also the diagonals are of equal length and base angles are congruent.

A kite is a quadrilateral with two pairs of adjacent sides is equal in length. One pair of opposite angles is equal in measure. The two diagonals of a kite are perpendicular and bisect each other.

Here are the important properties to remember:

This mini-lesson is on special types of quadrilaterals. So far the focus of learning was on properties of quadrilaterals. Now you'll explore, with the help of some examples and solution, how these properties and knowledge will be used for special quadrilaterals- a parallelogram, rectangle, square, rhombus, trapezoid, an isosceles trapezoid and kites.

A parallelogram is a quadrilateral, if both pairs of opposite sides are equal and parallel to each other. Also in case of parallelogram, opposite sides and opposite angles are congruent and diagonals bisect each other.

A rectangle is a parallelogram with four right angles. Opposite sides of a rectangle are parallel and equal. The diagonals of a rectangle are congruent. A square is rectangle with four congruent sides. Opposite sides of a square are parallel and all sides are equal in length and all angles are equal to 90°.

A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel and opposite angles are equal. The diagonals of a rhombus are perpendicular and bisect each other.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is a quadrilateral where two opposite sides are parallel, the two other sides are of equal length. Also the diagonals are of equal length and base angles are congruent.

A kite is a quadrilateral with two pairs of adjacent sides is equal in length. One pair of opposite angles is equal in measure. The two diagonals of a kite are perpendicular and bisect each other.

Here are the important properties to remember:

- All quadrilaterals have 4 sides.
- A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees).
- A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles are equal.
- The rectangle (oblong) contains 4 right angles (an angle of 90?). It has got 2 pairs of equal length sides.
- A parallelogram is a rectangle that has been pushed over. Opposite sides are the same length and they are parallel.
- A trapezium has got one pair of parallel sides.
- A kite as got two pairs of sides next to each other that have equal length.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

- Mathematics > General
- Mathematics > Geometry
- Education > General

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Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories;