Cathetus


Cathetus

:"This page is about the geometric meaning. For the plant, see "Phyllanthus". For the epiplemiine moth, see "Monobolodes.

In a right triangle, the cathetus (originally from the Greek word _el. Κάθετος, plural _el. Κάθετοι; its plural in English is "catheti" because it comes more directly from the Latin transliteration "cathetus", whose plural is such) is either one of the two sides which are adjacent to the right angle. The remaining side, opposite the right angle, is called the hypotenuse. The cathetus is far more frequently known as a "leg" of the right triangle, or by the periphrasis "side about the right angle". When they are related to the hypotenuse, the catheti are often referred to simply as "the other two sides".

The ratio of the lengths of the catheti defines the trigonometric functions tangent and cotangent of the angles in the triangle. In a right triangle, the length of the cathetus is also the geometric mean between the length of the segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.

If a right triangle is not isosceles (i.e. it is scalene), then its catheti have different lengths and a distinction can be made between the "minor" one and the "major" one.

In an isosceles triangle, the cathetus of the triangle are the two congruent sides of the triangle.

By the Pythagorean theorem, the sum of the areas of the squares on the catheti is equal to the area of the square on the hypotenuse. Equivalently, the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse.

Generally

In a wider sense, a cathetus is any line falling perpendicularly on another line or a surface. Such a line is more commonly known as a surface normal.

References

* Bernhardsen, T. Geographic Information Systems: An Introduction, 3rd ed. New York: Wiley, p. 271, 2002.

ee also

* Right triangle
* Hypotenuse
* Pythagorean theorem
* Isosceles triangle

External links

*


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Cathetus — Cath e*tus, n.; pl. {catheti}. [L., fr. Gr. ? a perpendicular line, fr. ? let down, fr. ?. See {Catheter}.] (Geom.) One line or radius falling perpendicularly on another; as, the catheti of a right angled triangle, that is, the two sides that… …   The Collaborative International Dictionary of English

  • Cathĕtus — (gr.), senkrechte Linie, s. Katheter; bes. 1) (Phys.), C. incidentĭae, die von einem ausstrahlenden Punkt auf die reflectirende (od. dieselbe als verlängert gedachte) Fläche gezogene Gerade; C. reflexiōnis, eine die Richtung des zurückgeworfenen… …   Pierer's Universal-Lexikon

  • cathetus — /kath i teuhs, keuh thee teuhs/, n., pl. catheti / tuy , tuy/. (in an Ionic capital) the vertical guideline through the eye of a volute, from which the form of the volute is determined. [1565 75; < L (n.) < Gk káthetos perpendicular, equiv. to… …   Universalium

  • cathetus — noun /ˈkæ.θɪ.təs,kəˈθɪ.təs/lang=en A line perpendicular to a surface (or line); in particular, either of the sides of a right triangle other than its hypotenuse. Syn: leg …   Wiktionary

  • cathetus — n. line or radius falling perpendicularly on another; side of a right angled triangle that makes a right angle with another one (Geometry) …   English contemporary dictionary

  • cathetus — /kath i teuhs, keuh thee teuhs/, n., pl. catheti / tuy , tuy/. (in an Ionic capital) the vertical guideline through the eye of a volute, from which the form of the volute is determined. [1565 75; < L (n.) < Gk káthetos perpendicular, equiv …   Useful english dictionary

  • catheti — Cathetus Cath e*tus, n.; pl. {catheti}. [L., fr. Gr. ? a perpendicular line, fr. ? let down, fr. ?. See {Catheter}.] (Geom.) One line or radius falling perpendicularly on another; as, the catheti of a right angled triangle, that is, the two sides …   The Collaborative International Dictionary of English

  • cateto — (De origen incierto.) ► sustantivo despectivo Persona ignorante y tosca: ■ es y será siempre un cateto. SINÓNIMO palurdo (Del lat. cathetus < gr. kathetos, perpendicular.) ► sustantivo masculino GEOMETRÍA Cada uno de los dos lados que forman… …   Enciclopedia Universal

  • Triangle — This article is about the basic geometric shape. For other uses, see Triangle (disambiguation). Isosceles and Acute Triangle redirect here. For the trapezoid, see Isosceles trapezoid. For The Welcome to Paradox episode, see List of Welcome to… …   Wikipedia

  • Manezhnaya Square, Saint Petersburg — For other uses, see Manezhnaya Square. 59°56′9″N 30°20′25″E / 59.93583°N 30.34028°E / 59.93583; 30.34028 Manezhnaya Square (Russian …   Wikipedia