# Right Angle

Topics

- Why is it called a
*right*angle? Are there*left*angles or*wrong*angles? - Making a right angle by paperfolding.

Informally, a right angle is the angle at the corner of a (rectangular) piece of paper. Other examples include the angle at the base of a capital L or the top of a capital T. The measure of a right angle, in degrees, is 90°.

## Meaning

**Informa**l: an angle that matches the corner of a (rectangular) piece of paper, or the angle at the base of a capital L or the top of a capital T.

These are all examples of right angles:

These are not right angles: The two at the left are both obtuse ("wider" than a right angle) and the two at the right are both acute ("sharper" than a right angle).

## Paperfolding to construct a right angle

You can construct a right angle just by folding paper, even one that has been ripped so that there are no straight edges!

In any direction, fold the piece of paper. For example:

The result will look like this:

Then make a second fold, being careful that the original crease lies on top of itself.

The result will look like this:

When you unfold the piece of paper, the two creases will be perpendicular to each other. The four angles are all right angles.

**Why does this work?** The first fold creates a straight-line crease. The second fold folds one part of that line onto the other. If an angle is folded through its vertex so that one side of the angle lies directly on the other, the fold bisects the angle. The straight line of the original crease forms a straight angle (180°) around any point on it. Folding through that point bisects the angle, so the resulting angles are each 90°, and so they are right angles.

## Related mathematical ideas

- In informal speech (not mathematics), right-angle corners are sometimes called
*square*corners even though no complete square may exist (as in the examples above). - Four right angles
*fit*around a point; for example, when we draw two diameters to cut a circle into fourths, the four angles that fit around the center of the circle are right angles. - The way we define degrees, a "full turn" around a point is 360°, so the measure of each right angle is one fourth of that: 90°.
- Two lines that are at right angles to each other are said to be perpendicular to each other.
- The word-parts
*rect-*and*-angle*in"rectangle" literally mean "right angle."

## What's in a word?

The gh in "ri**gh**t" was once pronounced; it descended from the c in Latin "re**c**t-." In English, words with "rect-" in them, like * rectangle*, often have meanings related to "right."

*Right* has many meanings

One of its meanings is 'cor**rect**,' the opposite of 'wrong.' (When we get something wrong, we try to **rect**ify our error.) Another meaning is the opposite of 'left.' Still another meaning is 'straight' or 'di**rect**ly,' as in "After school, please come *right* home."

**Why all those meanings? What do they all have in common?** Like most words, *right* has great-…-great grandparents. The earliest ancestor we know might have sounded something like *reg*, and many of *right'*s cousins are spelled like *reg* or *rect*.

The original meaning was something like 'to move in a straight line.' When we **reg**ulate something, we are keeping it on track, keeping it from changing, keeping control. 'Following the straight path' means doing the 'right' thing. The person who gets to make all the **ru**les and **reg**ulations that keep people in line is the king. The Latin word for king is 'rex,' related to *reg* and *rect*. Tyrannosaurus *Rex* was 'king' of the dinosaurs.

When the g in * regular* fades into a vowel, we get its cousin,

*.*

**ru**lerThe g fades into a vowel in many English words. In words like

lightandthoughand many otherghwords, the g stays in the spelling, but just disappears in pronunciation. In some words, likeruleandroyal, it even drops out of the spelling.Royalisregal(from 'rex' the king) with a vowel-like g. When wedrawan answer out of someone, we aredragging it, with a vowel-like g! And look up the meaning ofdray.That also comes fromdraging.Guardianandwardenand evenyardare related the same way.

When the *g* in *regular* is silent (as it is in *right*, and many other words), we get *ruler*. A *ruler* helps you draw a straight line.

The * royal*,

*king was the*

**reg**al**rich**est (yes, that's related, too), most powerful person, who gave people their

*rights*, or took them away! When we name children

**Rich**ard or

**Reg**ina or, of course,

**Rex**—or Hen

**ry**or

**Roy**with yet another silent

*g*—we are comparing them to kings and queens!

**If right means something like 'straight,' why do we say right turn?** Rex, the

**roy**al,

**ru**ling king, is strong, and so

*right*suggests strength. The strong hand, for most people, is their

*right*hand, so a turn

*to the right*is a turn toward that strong right hand.

### Where does a *right* angle get its name? Are there "left angles," too?

No, the **right angle** has nothing to do with right or left turns.

In this map, we say that Walnut Street makes a *right angle* with Main Street because it goes as '*straight' away* from Main Street as possible. Corn Street veers off at a different angle.