https://esl.proz.com/kudoz/spanish-to-english/mathematics-statistics/6211118-teorema-del-cateto.html?paging=y
This site uses cookies. Some of these cookies are essential to the operation of the site, while others help to improve your experience by providing insights into how the site is being used. For more information, please see the ProZ.com privacy policy.
Cookie settings
protocolo visible a su inicio
Toma de FA y FP
Oct 20, 2016 00:23
8 yrs ago
3 viewers *
español term

TEOREMA DEL CATETO

español al inglés Ciencias Matemáticas y estadística algebra
This is talking about right triangles, and after describing the Pythagorean theorem and altitude theorem, it talks about the "teorema del cateto". Leg/side/cathetus theorem? I haven't found it anywhere. Thanks!
Proposed translations (inglés)
4 +1 the cathetus theorem
4 +1 Right Triangle Altitude Theorem
4 "Leg rule" for right-angled triangles.
References
Right Triangle Leg Leg Congruence Theorem / Hypotenuse-Leg (HL) for Right Triangles
Cateto
Leg rule

Discussion

Helena Chavarria Oct 20, 2016:
@Neil 'La otra posibilidad, que es la que más parece convencer a Corominas, es que cateto sea una alteración popular de *pateto, quizá influida por otras voces, puesto que existe una voz portuguesa "pateta" (necio), y otras voces de sentido parecido, como patán, que se hacen derivar de pata, vocablo de origen incierto y bastante discutido'.

http://etimologias.dechile.net/?cateto
DLyons Oct 20, 2016:
@Neil The DRAE doesn't know how that came about, so I certainly don't.

There's a note saying "Cathetus is a cant word fur puritan" relative to
Yet these the mates of Cathetus,
From whome good Lord deliver us!

In Spanish, it goes back to at least 1923 (and probably much ealier)
"Güeno, pus ya llegó un cateto que dijo:"
neilmac Oct 20, 2016:
Cuidado con el borde... ¡el cateto soy yo! This is all Greek to me... :-) Seriously though, I wonder how the word came to mean "numbskull/dunderhead"? Perhaps it is shorter (más corto) than the other parts of the triangle?
Charles Davis Oct 20, 2016:
1. "Teorema del cateto
En todo triángulo rectángulo el cuadrado de un cateto es igual al producto de la hipotenusa por la proyección ortogonal de ese cateto sobre la hipotenusa"
https://es.wikipedia.org/wiki/Triángulo_rectángulo#Teorema_d...

2. "The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles"
http://www.mathwarehouse.com/geometry/congruent_triangles/hy...

These are clearly not the same theorem.

Proposed translations

+1
37 minutos
Selected

the cathetus theorem

In a right triangle, the length of a cathetus is the geometric mean of the length of the adjacent segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.

--------------------------------------------------
Note added at 39 mins (2016-10-20 01:03:32 GMT)
--------------------------------------------------

In a right triangle, the length of a cathetus is the geometric mean of the length of the adjacent segment cut by the altitude to the hypotenuse and the length of the whole hypotenuse.

--------------------------------------------------
Note added at 41 mins (2016-10-20 01:05:16 GMT)
--------------------------------------------------

http://www.vitutor.com/geo/eso/as_3.html
Peer comment(s):
agree Charles Davis : Though the expression is uncommon in English
39 minutos
Thanks, Charles!
neutral DLyons : Technically this is perfectly correct.
5 horas
Something went wrong...
4 KudoZ points awarded for this answer. Comment: "Thank you!"
+1
6 horas

Right Triangle Altitude Theorem

The word cathetus will mean something only to a handful of English speakers. Its statement is dry to the point of being unintelligble to most people. It's Theorem 11 at https://books.google.fr/books?id=LLXxBwAAQBAJ&pg=PA22 but wisely they just give a diagram.


--------------------------------------------------
Note added at 6 hrs (2016-10-20 07:00:34 GMT)
--------------------------------------------------

Or Geometric Mean Theorem
https://en.wikipedia.org/wiki/Geometric_mean_theorem
Reference:

http://mathworld.wolfram.com/Cathetus.html

Peer comment(s):
neutral Charles Davis : It's essentially the so-called "leg rule" part of the geometric mean (altitude) theorem: hypot/leg = leg/segment so leg^2 = hypot x segment: the latter is the teorema del cateto. ST lists altitude theorem separately, so must distinguish.
19 minutos
Thanks Charles. The term "leg rule" is used. I'd avoid cathetus. // P.S. I suggest you post it as an answer.
agree Helena Chavarria : Leg Rule. http://www.mathsisfun.com/geometry/mean-proportional.html
6 horas
Thanks Helena. The etymology you give is interesting!
Something went wrong...
2 días 9 horas

"Leg rule" for right-angled triangles.

Just for the sake of the Glossary.

If Charles or Helena care to post the same answer I'll withdraw this :-)
Something went wrong...

Reference comments

52 minutos
Reference:

Right Triangle Leg Leg Congruence Theorem / Hypotenuse-Leg (HL) for Right Triangles

The Right Triangle Leg Leg Congruence Theorem - Proofs from The ...
proofsfromthebook.com/.../leg-leg-congruence-theo...
17 dic. 2013 - The Right Triangle Leg Leg Congruence Theorem is a theorem for right triangles that says if the two corresponding shorter legs of two right ...

Hypotenuse-Leg (HL) for Right Triangles
https://www.math.washington.edu/.../hypleg.html
Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. Using words: In words, if the ...

The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples ...
study.com/academy/lesson/the-hl-theorem.html
In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two...
Peer comments on this reference comment:
neutral DLyons : But along the right lines!
5 horas
neutral Charles Davis : This is a different theorem. The teorema del cateto is not a congruence theorem.
5 horas
Something went wrong...
7 horas
Reference:

Cateto

This usage is new to me, as I had only ever come across the word to mean "idiot", as in the Alfredo Landa movie 'Cateto a Babor'...
Reference:

http://www.dailymotion.com/video/x3m43fy

https://es.oxforddictionaries.com/traducir/espanol-ingles/cateto

Something went wrong...
13 horas
Reference:

Leg rule

Altitude rule:

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

Leg rule:

Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.

http://www.regentsprep.org/regents/math/geometry/gp12/lmeanp...

Teorema de la altura:

En un triángulo rectángulo, la altura relativa a la hipotenusa es media proporcional entre los 2 segmentos que dividen a ésta.

Teorema del cateto:

En todo triángulo rectángulo un cateto es media proporcional entre la hipotenusa y su proyección sobre ella.

http://www.vitutor.com/geo/eso/s_6.html
Peer comments on this reference comment:
agree Charles Davis : It seems to be a good match, and "cathetus theorem" is conspicuously absent from EN maths teaching materials on right-angled triangle theorems.
3 horas
My retired teaching hubbie wasn't in the mood to explain. He just said that depending on the data you have, you apply the rule or theorem you need. I think Right Triangle Altitude Theorem comprises a set of rules/theorems. Thank you, Charles!
Something went wrong...