Quadrilaterals

Quadrilaterals

Quadrilateral but ways "four sides"
(quad means four, lateral means side).

A Quadrilateral has four-sides, information technology is 2-dimensional (a flat shape), airtight (the lines bring together up), and has straight sides.

Try it Yourself

geometry/images/geom-quad.js?style=choose

(Also come across this on Interactive Quadrilaterals)

Backdrop

A quadrilateral has:

  • four sides (edges)
  • 4 vertices (corners)
  • interior angles that add to 360 degrees:

Quadrilateral Angles

Effort drawing a quadrilateral, and measure out the angles. They should add together to 360°

Types of Quadrilaterals

There are special types of quadrilateral:

Types of Quadrilateral

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms . See below for more details.

Let us look at each type in turn:

The Rectangle

Rectangle
the piddling squares in each corner mean "correct angle"

A rectangle is a iv-sided shape where every angle is a right angle (90°).

As well opposite sides are parallel and of equal length.

The Foursquare

Square
the little squares in each corner hateful "right angle"

A square has equal sides (marked "s") and every bending is a right angle (xc°)

Also contrary sides are parallel.

A foursquare besides fits the definition of a rectangle (all angles are xc°), and a rhombus (all sides are equal length).

The Rhomb

Rhombus

A rhombus is a 4-sided shape where all sides have equal length (marked "s").

Also contrary sides are parallel and opposite angles are equal.

Rhombus Diagonals

Another interesting matter is that the diagonals (dashed lines) come across in the middle at a right angle. In other words they "bisect" (cut in half) each other at correct angles.

A rhomb is sometimes called a rhombus or a diamond.

The Parallelogram

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).

Annotation: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

Square

A parallelogram with:

  • all sides equal and
  • angles "A" and "B" equally right angles

is a square!

The Trapezoid (Britain: Trapezium)

Trapezoid (or Trapezium) Trapezoid (or Trapezium)

Trapezoid

Isosceles Trapezoid

A trapezoid (chosen a trapezium in the UK) has a pair of opposite sides parallel.

And a trapezium (called a trapezoid in the UK) is a quadrilateral with NO parallel sides:

Trapezoid Trapezium
In the U.s.a.: a pair of parallel sides NO parallel sides
In the Uk: NO parallel sides a pair of parallel sides
(the U.s.a. and Great britain definitions are swapped over!)

An Isosceles trapezoid, every bit shown higher up, has left and right sides of equal length that join to the base at equal angles.

The Kite

The Kite

Hey, it looks like a kite (unremarkably).

It has two pairs of sides:

Each pair is made of two equal-length sides that join up.

Also:

  • the angles where the two pairs run across are equal.
  • the diagonals, shown as dashed lines above, come across at a right angle.
  • one of the diagonals bisects (cuts equally in one-half) the other.

... and that'south it for the special quadrilaterals.

Irregular Quadrilaterals

The only regular (all sides equal and all angles equal) quadrilateral is a square. And so all other quadrilaterals are irregular.

The "Family unit Tree" Chart

Quadrilateral definitions are inclusive.

Case: a foursquare is also a rectangle.

So we include a square in the definition of a rectangle.

(We don't say "Having all 90° angles makes it a rectangle except when all sides are equal then it is a square.")

This may seem odd, every bit in daily life we think of a square as non being a rectangle ... merely in mathematics it is.

Using the chart below nosotros can respond such questions equally:

  • Is a Foursquare a type of Rectangle? (Yes)
  • Is a Rectangle a type of Kite? (No)

Quadrilateral Classification

Complex Quadrilaterals

Oh Yes! when 2 sides cross over, we telephone call it a "Circuitous" or "Cocky-Intersecting" quadrilateral, like these:

Complex Quadrilaterals

They still have 4 sides, but two sides cantankerous over.

Polygon

A quadrilateral is a polygon. In fact it is a four-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a v-sided polygon, and then on.

Play with Them

Now that you know the different types, you tin play with the Interactive Quadrilaterals.

Other Names

A quadrilateral can sometimes exist chosen:

  • a Quadrangle ("4 angles"), so it sounds like "triangle"
  • a Tetragon ("four polygon"), and so information technology sounds like "pentagon", "hexagon", etc.

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