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TEOREMA DEL CATETO

English translation: the cathetus theorem

00:23 Oct 20, 2016
Spanish to English translations [PRO]
Science - Mathematics & Statistics / algebra
Spanish term or phrase: TEOREMA DEL CATETO
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!
maryblack
United States
Local time: 02:39
English translation:the cathetus theorem
Explanation:
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.

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Note added at 39 mins (2016-10-20 01:03:32 GMT)
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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)
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http://www.vitutor.com/geo/eso/as_3.html
Selected response from:

Francois Boye
United States
Local time: 03:39
Grading comment
Thank you!
4 KudoZ points were awarded for this answer



Summary of answers provided
4 +1the cathetus theorem
Francois Boye
4 +1Right Triangle Altitude Theorem
DLyons
4"Leg rule" for right-angled triangles.
DLyons
Summary of reference entries provided
Right Triangle Leg Leg Congruence Theorem / Hypotenuse-Leg (HL) for Right Triangles
andres-larsen
Cateto
neilmac
Leg rule
Helena Chavarria

Discussion entries: 4





  

Answers


37 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +1
the cathetus theorem


Explanation:
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

Francois Boye
United States
Local time: 03:39
Specializes in field
Native speaker of: Native in FrenchFrench
PRO pts in category: 72
Grading comment
Thank you!

Peer comments on this answer (and responses from the answerer)
agree  Charles Davis: Though the expression is uncommon in English
39 mins
  -> Thanks, Charles!
neutral  DLyons: Technically this is perfectly correct.
5 hrs
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6 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +1
Right Triangle Altitude Theorem


Explanation:
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.


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Note added at 6 hrs (2016-10-20 07:00:34 GMT)
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Or Geometric Mean Theorem
https://en.wikipedia.org/wiki/Geometric_mean_theorem


    Reference: http://mathworld.wolfram.com/Cathetus.html
DLyons
Ireland
Local time: 08:39
Specializes in field
Native speaker of: English
PRO pts in category: 263

Peer comments on this answer (and responses from the answerer)
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 mins
  -> 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 hrs
  -> Thanks Helena. The etymology you give is interesting!
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2 days 9 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
"Leg rule" for right-angled triangles.


Explanation:
Just for the sake of the Glossary.

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

DLyons
Ireland
Local time: 08:39
Specializes in field
Native speaker of: English
PRO pts in category: 263
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Reference comments


52 mins
Reference: Right Triangle Leg Leg Congruence Theorem / Hypotenuse-Leg (HL) for Right Triangles

Reference information:
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...

andres-larsen
Venezuela
Native speaker of: Native in EnglishEnglish
PRO pts in category: 4

Peer comments on this reference comment (and responses from the reference poster)
neutral  DLyons: But along the right lines!
5 hrs
neutral  Charles Davis: This is a different theorem. The teorema del cateto is not a congruence theorem.
5 hrs
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7 hrs
Reference: Cateto

Reference information:
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
neilmac
Spain
Native speaker of: Native in EnglishEnglish
PRO pts in category: 32
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13 hrs peer agreement (net): +1
Reference: Leg rule

Reference information:
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

Helena Chavarria
Spain
Native speaker of: Native in EnglishEnglish
PRO pts in category: 12

Peer comments on this reference comment (and responses from the reference poster)
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 hrs
  -> 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!
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