Quadrilaterals

Quadrilaterals

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

A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join upwardly), and has straight sides.

Endeavour it Yourself

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

(Also see this on Interactive Quadrilaterals)

Backdrop

A quadrilateral has:

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

Quadrilateral Angles

Endeavour cartoon a quadrilateral, and measure the angles. They should add to 360°

Types of Quadrilaterals

At that place are special types of quadrilateral:

Types of Quadrilateral

Some types are too included in the definition of other types! For instance a square, rhomb and rectangle are besides parallelograms . See below for more than details.

Let united states of america wait at each blazon in plow:

The Rectangle

Rectangle
the little squares in each corner hateful "correct angle"

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

Too opposite sides are parallel and of equal length.

The Square

Square
the picayune squares in each corner mean "correct angle"

A square has equal sides (marked "s") and every angle is a correct angle (90°)

Also opposite sides are parallel.

A square likewise fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

The Rhombus

Rhombus

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

Also opposite sides are parallel and reverse angles are equal.

Rhombus Diagonals

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

A rhombus is sometimes called a rhomb or a diamond.

The Parallelogram

Parallelogram

A parallelogram has reverse sides parallel and equal in length. Also opposite angles are equal (angles "A" are the aforementioned, and angles "B" are the same).

Note: Squares, Rectangles and Rhombuses are all Parallelograms!

Instance:

Square

A parallelogram with:

  • all sides equal and
  • angles "A" and "B" every bit right angles

is a square!

The Trapezoid (UK: Trapezium)

Trapezoid (or Trapezium) Trapezoid (or Trapezium)

Trapezoid

Isosceles Trapezoid

A trapezoid (called 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 US and U.k. definitions are swapped over!)

An Isosceles trapezoid, as shown above, 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 (usually).

It has two pairs of sides:

Each pair is made of ii equal-length sides that join upwardly.

Besides:

  • the angles where the two pairs run across are equal.
  • the diagonals, shown as dashed lines above, meet at a right bending.
  • i of the diagonals bisects (cuts every bit in half) the other.

... and that's 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 Tree" Nautical chart

Quadrilateral definitions are inclusive.

Instance: a foursquare is besides a rectangle.

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

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

This may seem odd, equally in daily life we think of a foursquare every bit not being a rectangle ... but in mathematics it is.

Using the nautical chart beneath we can answer such questions as:

  • Is a Square a type of Rectangle? (Yeah)
  • Is a Rectangle a blazon of Kite? (No)

Quadrilateral Classification

Complex Quadrilaterals

Oh Yes! when 2 sides cantankerous over, we call it a "Complex" or "Self-Intersecting" quadrilateral, like these:

Complex Quadrilaterals

They notwithstanding have 4 sides, but two sides cross over.

Polygon

A quadrilateral is a polygon. In fact it is a iv-sided polygon, merely like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and then on.

Play with Them

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

Other Names

A quadrilateral tin sometimes be chosen:

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

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