# Basic Geometry

### Topics

## Introduction to :

Quadrilaterals are four sided shapes. The most common include squares and rectangles, but there are loads of others as well. Like triangles, they are classified by their angles and sides.

In this section we are going to cover the six common quadrilaterals that you see all the time.

**Parallelogram**

- Parallelograms are all quadrilaterals where the opposite sides are parallel.

All of these are parallelograms:

There are many special properties of parallelograms. Here are the ones you probably need to know.

Opposite sides are parallel. | |

Opposite angles are congruent. | |

Opposite sides are congruent. | |

Adjacent angles are supplementary. |

**Rectangle**

- All four-sided figures with two sets of parallel sides and four 90° angles are called rectangles. Here are two different rectangles:

Now let's look at all the properties of rectangles.

Opposite sides are parallel. | |

All angles are 90°. | |

Opposite sides are congruent. | |

Adjacent angles are supplementary. |

**Rhombus**

- A rhombus has two sets of parallel sides and all sides must be congruent. These are rhombi:

Here are the properties of a rhombus:

Opposite sides are parallel. | |

Opposite angles are congruent. | |

All sides are congruent. | |

Adjacent angles are supplementary. |

**Square**

- Every parallelogram with four congruent sides and four 90° angles is a square.

These are the properties of squares:

Opposite sides are parallel. | |

All angles are 90 degrees. | |

All sides are congruent. | |

Adjacent angles are supplementary. |

**Trapezoid**

- Trapezoids have only one set of parallel sides. If the two legs are congruent, then it is called an isosceles trapezoid.

These are the properties of all trapezoids:

There is only one set of parallel sides. | |

There are only two sets of adjacent supplementary angles. | |

These properties only apply to isosceles trapezoids: | |

There is only one set of congruent sides. | |

There are two sets of congruent angles |

**Kite**

Kites (also known as a **deltoid**) are quadrilaterals with two sets of congruent sides. Unlike a parallelogram, these sides are adjacent. It looks like (gasp) a kite!

These are the properties of kites:

There are only two sets of congruent adjacent sides. | |

There is only one set of congruent angles. |

It can be kind of difficult to keep track of what is what, so here it is charted out:

And, if you're really a visual person, here's a Venn diagram.

As you can see, all of these are quadrilaterals, but rectangles and rhombi are also parallelograms, and squares are also parallelograms, rectangles, and rhombi. Kites and trapezoids are lonely islands floating by themselves.

**Regular Quadrilateral**

No surprise here is that the most common quadrilateral, the square, is also **regular**. It has four congruent sides and four congruent angles (90°).

#### Classifications

Classify each shape based on the description. Be sure to include every possible answer: *parallelogram, rectangles, rhombus, square, trapezoid, and kite.*

#### Exercise 1

A quadrilateral with opposite sides parallel.

#### Exercise 2

A quadrilateral with four congruent sides.

#### Exercise 3

A quadrilateral with two sets of congruent sides.

#### Exercise 4

A quadrilateral with exactly one set of parallel sides.

#### Exercise 5

A quadrilateral with one set of congruent angles.

#### Exercise 6

A quadrilateral with two or more sets of supplementary angles.

#### Fill in the Blanks

Fill in each blank with *always, sometimes*, or *never.*

#### Exercise 7

A square is ____________ a rectangle.

#### Exercise 8

A kite is __________ a parallelogram.

#### Exercise 9

A trapezoid is ____________ a quadrilateral.

#### Exercise 10

A rhombus is ___________ a square.