QUADRILATERALS

UNIT 06: POLYGONS

01. QUADRILATERALS

It is difficult to classify quadrilaterals, so as an introduction to this subject, I quote the definition of quadrilaterals which makes Euclid in his book “The Elements”

“Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.”

Quadrilateral just means “four sides”. Any four-sided shape is a quadrilateral, but the sides have to be straight, and it has to be 2-dimensional. A quadrilateral is polygon with four corners or vertices and four sides or edges which are line segments. Quadrilaterals can have different shapes, but all of them have four vertices and two diagonals and the sum of all the internal angles is 360º in the simple ones.

There are simple and complex quadrilaterals, we will only study the simple ones. They still have 4 sides, but two sides cross over.

Simple-Complejo

Types of quadrilaterals

Quadrilaterals are divided into convex and concave.

  • A quadrilateral is convex, when none of its internal angles is bigger than 180º.
  • A quadrilateral is concave, when one of its internal angles is bigger than 180º.

Convex quadrilaterals

A. Parallelograms
A Parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal. Parallelograms are divided into:

    1. Right: All their internal angles are equal to 90º.

RECTANGULOS

      • Square: All its sides are equal.

Area-cuadrado

      • Rectangle: Its sides are equal two by two.

Area-rectangulo

  1. Other: Their internal angles are equal two by two, opposite internal angles are equal, two internal angles are obtuse and two internal angles are acute.

OBLICUANGULOS

  • Rhombus: All its sides are equal.

Area-rombo

  • Rhomboid: Its sides are equal two by two.

Area-rectangulo

Trapezoid

Trapezium

US

a pair of parallel sides

NO parallel sides

UK

NO parallel sides

a pair of parallel sides

B. Trapeziums (UK) / Trapezoids (US)
A Trapezium is a quadrilateral with two parallel sides and the other sides are not parallel to each other. The distance between parallel sides is called height.
Area-trapecio
Trapeziums are divided into:
TRAPECIOS

  1. Rights: One of its parallel sides is perpendicular to the parallel sides.
  2. Isosceles: Non parallel sides are equal.
  3. Scalenes: Non parallel sides are different.

C. Trapezoids (UK) / Trapeziums (US)
A Trapezoid is a quadrilateral with no parallel sides.
TRAPEZOIDES
Link to this app to practise quadrilaterals properties.

One thought on “QUADRILATERALS

  1. Pingback: SECOND TERM | Blog de Educación Plástica y Visual

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s