A quadrilateral is a closed figure with four straight sides. You can make a quadrilateral by taking (or imagining) anything straight and thin you might have handy: pens, toothpicks, chopsticks, etc. A square is one type of a special quadrilateral.

Quadrilateral just means “four sides”

(*quad* means four, *lateral *means side).

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

**Properties**

A quadrilateral has:

- four sides (edges)
- four vertices (corners)
- interior angles that add to
**360 degrees**:

**Exercise**

Try drawing a quadrilateral, and measure the angles. They should add to **360°**

**Types of Quadrilaterals**

There are special types of quadrilateral:

Some types are also included in the definition of other types! For example a **square**, **rhombus** and **rectangle** are also ** parallelograms**.

Let us look at each type in turn:

**The Rectangle**

means “right angle” | |||

and | show equal sides | ||

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

Also **opposite sides** are parallel and of equal length.

**The Rhombus**

A rhombus is a four-sided shape where all sides have equal length.

Also opposite sides are parallel *and* opposite angles are equal.

Another interesting thing is that the diagonals (dashed lines in second figure) meet in the middle at a right angle. In other words they “bisect” (cut in half) each other at right angles.

A rhombus is sometimes called a **rhomb** or a **diamond**.

**The Square**

means “right angle” | |||

show equal sides | |||

A square has equal sides and every angle is a right angle (90°)

Also opposite sides are parallel.

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

**The 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).

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

**Example:**

A **parallelogram** with:

- all sides equal and
- angles “a” and “b” as right angles

is a **square**!

**The Trapezoid/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 US: | a pair of parallel sides | NO parallel sides |

In the UK: | NO parallel sides | a pair of parallel sides |

(the US and UK 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**

Hey, it looks like a kite (usually).

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 meet are equal.
- the diagonals, shown as dashed lines above, meet at a right angle.
- one of the diagonals
*bisects*(cuts equally 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. So all other quadrilaterals are **irregular**.

**The “Family Tree” Chart**

Quadrilateral definitions are **inclusive**.

**Example: a square is also a rectangle.**https://googleads.g.doubleclick.net/pagead/ads?guci=2.2.0.0.2.2.0.0&client=ca-pub-1661929042807246&output=html&h=280&slotname=9757662299&adk=416771370&adf=2768648106&pi=t.ma~as.9757662299&w=700&fwrn=4&fwrnh=100&lmt=1604309646&rafmt=1&psa=1&format=700×280&url=http%3A%2F%2Fstoplearn.com%2Fcourses%2Fsecondary-school%2Fjss2-second-term-basic-technology-junior-secondary-school%2Flessons%2Fquadrilaterals%2F&flash=0&fwr=0&fwrattr=true&rpe=1&resp_fmts=3&wgl=1&adsid=ChAIgPn-_AUQkJWp-eO5jtJNEkgAMWjS4M82Y6pcyVlsvJo4rLAchUMSuzz8-GT7dd5X676fMlzH2dtq4UhjTTcYNXyzJMfGneUrUBXwbPUvgQNoXt8Y2f2dD9A&tt_state=W3siaXNzdWVyT3JpZ2luIjoiaHR0cHM6Ly9hZHNlcnZpY2UuZ29vZ2xlLmNvbSIsInN0YXRlIjowfSx7Imlzc3Vlck9yaWdpbiI6Imh0dHBzOi8vYXR0ZXN0YXRpb24uYW5kcm9pZC5jb20iLCJzdGF0ZSI6MH1d&dt=1604309619554&bpp=10&bdt=159&idt=112&shv=r20201029&cbv=r20190131&ptt=9&saldr=aa&abxe=1&cookie=ID%3D3b5c0a4b352ccd7b-2255262b41a60032%3AT%3D1602230088%3ART%3D1602230088%3AS%3DALNI_MaWUG7yiaaHthyGgrREyU5I0uWdRw&prev_fmts=0x0%2C1200x90_0ads_al&nras=1&correlator=7818172716258&frm=20&pv=1&ga_vid=1300243797.1604309620&ga_sid=1604309620&ga_hid=176727478&ga_fc=0&iag=0&icsg=599886135210&dssz=59&mdo=0&mso=0&u_tz=60&u_his=20&u_java=0&u_h=768&u_w=1366&u_ah=728&u_aw=1366&u_cd=24&u_nplug=3&u_nmime=4&adx=609&ady=658&biw=1518&bih=667&scr_x=0&scr_y=0&eid=21066922&oid=3&psts=AGkb-H-ugxHRqvUGENiri2BIZnLdH5w6PJpzzPVfFOWi4qPPWfUfo2puFA&pvsid=4371205875330035&pem=804&ref=http%3A%2F%2Fstoplearn.com%2Fcourses%2Fsecondary-school%2Fjss2-second-term-basic-technology-junior-secondary-school%2F&rx=0&eae=0&fc=896&brdim=0%2C0%2C0%2C0%2C1366%2C0%2C1366%2C728%2C1517%2C666&vis=1&rsz=%7C%7CaoeE%7C&abl=CA&pfx=0&fu=8320&bc=31&jar=2020-10-31-22&ifi=1&uci=a!1&fsb=1&xpc=Tw6NbWRwPA&p=https%3A//stoplearn.com&dtd=26579

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, as in daily life we think of a square as **not** being a rectangle … but in mathematics it **is**.

Using the chart below we can answer such questions as:

- Is a Square a type of Rectangle? (Yes)
- Is a Rectangle a type of Kite? (No)

**Complex Quadrilaterals**

Oh Yes! when two sides cross over, we call it a “Complex” or “Self-Intersecting” quadrilateral, like these:

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

**Polygon**

A quadrilateral is a polygon. In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.

**Other Names**

A quadrilateral can sometimes be called:

- a
**Quadrangle**(“*four angles*“), so it sounds like “triangle” - a
**Tetragon**(“*four*and*polygon*“), so it sounds like “pentagon”, “hexagon”, etc.

**ASSESSMENT**

- What is the name of this quadrilateral?

(a) kite

(b) square

(c) rhombus

(d) trapezium - What is the name of this quadrilateral?(a) trapezoid or trapezium

(b) kite

(c) parallelogram

(d) rhombus - What is the name of this quadrilateral?(a) kite

(b) parallelogram

(c) rhombus

(d) trapezoid or trapezium - What is the name of this quadrilateral?(a) parallelogram

(b) rectangle

(c) trapezoid or trapezium

(d) kite - One of these statements is
**not true**of kites

(a) it has two pairs of sides

(b) it has three pairs of sides

(c) the angles where the two pairs meet are equal

(d) one of the diagonals*bisects*(cuts equally in half) the other

Read our __disclaimer.__

AD: Take Free online baptism course: __Preachi.com__