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Basic Geometry
Basic Geometry
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Quadrilaterals

Red Quadrilateral

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:

    4 Parallelograms

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


    Opposite sides are parallel.Opposite Sides Are Parallel
    Opposite angles are congruent.Opposite Angles are Congruent Diagram
    Opposite sides are congruent.Opposite Sides are Congruent
    Adjacent angles are supplementary.

    Angle A + Angle B = 180 degrees

    Angle B + Angle C = 180 degrees

    Angle C + Angle D = 180 degrees

    Angle A + Angle D = 180

    Adjacent angles are supplementary parallelogram ABCD

Rectangle

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

2 Different Rectangles

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

    Opposite sides are parallel.Opposite Sides are Parallel Rectangle
    All angles are 90°.All angles are 90 degrees
    Opposite sides are congruent.Opposite sides are congruent
    Adjacent angles are supplementary.

    Angle A + Angle B = 180 degrees

    Angle B + Angle C = 180 degrees

    Angle C + Angle D = 180 degrees

    Angle A + Angle D = 180

    Adjacent angles are supplementary rectangle        

Rhombus

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

Rhombus and square

Here are the properties of a rhombus:

    Opposite sides are parallel.

    Properties of Rhombi - Opposite sides are parallel

    Opposite angles are congruent.

    Properties of Rhombi - opposite angles are congruent

    All sides are congruent.Properties of Rhombi - All sides are congruent
    Adjacent angles are supplementary. 

    Angle A + Angle B = 180 degrees

    Angle B + Angle C = 180 degrees

    Angle C + Angle D = 180 degrees

    Angle A + Angle D = 180

    Properties of Rhombi - adjacent angles are supplementary

Square

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

Square

These are the properties of squares:

    Opposite sides are parallel.Opposite sides are parallel square
    All angles are 90 degrees.Square # 2
    All sides are congruent.All sides congruent square
    Adjacent angles are supplementary.

    < A + < B = 180 degrees

    < B + < C = 180 degrees

    < C + < D = 180 degrees

    < A + < D = 180 degrees

    Adjacent Angles supplementary square ABCD

Trapezoid

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

2 Trapezoids

These are the properties of all trapezoids:

    There is only one set of parallel sides.One set of parallel sides trapezoid
    There are only two sets of adjacent supplementary angles.

    < A + < D = 180 degrees

    < B + < C = 180 degrees

    ABCD trapezoid
    These properties only apply to isosceles trapezoids:
    There is only one set of congruent sides.One set of congruent sides trapezoid
    There are two sets of congruent anglesTwo sets of congruent angles trapezoid

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!

2 Kites

These are the properties of kites:

    There are only two sets of congruent adjacent sides.Two sets of congruent adjacent sides Kite
    There is only one set of congruent angles. One set of congruent angles Kite

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

Quadrilateral Chart

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

Quadrilateral 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°).

Regular Quadrilateral

Next Page: Angles in a Polygon
Previous Page: Triangles

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