# Definition: 1.10: Right Angle, Perpendicular Straight Lines

And when a straight line stood upon (another) straight line makes adjacent angles (which are) equal1 to one another, each of the equal angles is a right angle, and the former straight line is called a perpendicular to that upon which it stands.

### Modern Definition

When one segment $$\overline{AC}$$ stands on another segment $$\overline{DB}$$ such that the angles $$\angle{BAC}$$ and $$\angle{CAD}$$ are congruent, then both angles are called right angles, and their legs (e.g. segments, straight lines or rays) are called perpendicular to each other.

For any two perpendicular segments $$\overline{AC}$$ and $$\overline{DB}$$ we write $$\overline{AC}\perp\overline{DB}$$.

Corollaries: 1

Thank you to the contributors under CC BY-SA 4.0!

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

1. Casey, John: "The First Six Books of the Elements of Euclid"

#### Bibliography

1. Knerr, Richard: "Knaurs Buch der Mathematik", Droemer Knaur Lexikographisches Institut, München, 1989

1. The word "equal" is an intuitive definition used by Euclid about 2,200 years ago. In modern mathematics, one would first define what "equal" angles actually mean. This could, for instance, be accomplished by defining the operation counter-clockwise rotation of a given segment $$\overline{BA}$$ around a fixed point $$A$$ and the traditional degree apportionment of a full rotation (identified with the perigon $= 360^\circ$), which was already introduced by the Ancient Babylonians. Two angles would be equal if they have the same portion of the perigon, measured in degrees. Another possibility is to talk about congruence.