im having trouble with the HL postulate.. how do you know when you have a leg? and how do you know when to use HL and not to get it mixed up with sss asa aas and sas? is the hypotenuse opposite from the 90 degree angle? what about cpctc?

Results 1 to 8 of 8

- April 18th 2005, 07:05 PM #1
## HL hypotenuse leg

im having trouble with the HL postulate.. how do you know when you have a leg? and how do you know when to use HL and not to get it mixed up with sss asa aas and sas? is the hypotenuse opposite from the 90 degree angle? what about cpctc?

- April 19th 2005, 02:27 AM #2

- Joined
- Apr 2005
- Posts
- 1,631

- April 19th 2005, 11:38 PM #3

- Joined
- Apr 2005
- Posts
- 35

If you have a right triangle, the side opposite the right angle is called the hypotenuse and the other two are called the legs. The Hypotenuse leg congruence theorem only applies if both of the triangles are right triangles. Basically, if you have two right triangles and they both have the same hypotenuse and the same leg, then the other leg must be the same as well. The other ones, SAS,SSS,ASA,SAA apply to any kind of triangle. Remember, only use HL on RIGHT triangles.

- April 21st 2005, 06:01 AM #4

- Joined
- Apr 2005
- Posts
- 16,816
- Thanks
- 1968

Originally Posted by**ticbol**

"HL" stands for "hypotenuse, leg". It only applies to RIGHT triangles (which are the only triangles that HAVE legs or hypotenuse!) unlike SSS, SAS, etc. The hypotenuse is always the longest side in a right triangle. If you are not given all lengths, the only way you can be certain that you have a hypotenuse and leg is if you are told that in the problem. Actually, since in a right triangle, all sides are related by the Pythagorean theorem, knowing any two sides give you the third: both "HL" and "LL" are equivalent to "SSS".

You shouldn't have any problem confusing HL with "ASA" because that requires that you know two angles! You shouldn't have any problem confusing HL with "SAS" (there is no "AAS") because those require that the angle be between the two sides- knowing that the triangle is a right triangle is the same as knowing one angle but it is not BETWEEN the leg and hypotenuse (the right angle is opposite the hypotenuse).

"HH" is, in fact, exactly the same as "SAS".

- April 21st 2005, 09:34 AM #5

- Joined
- Apr 2005
- Posts
- 1,631

- April 21st 2005, 12:43 PM #6
cpctc means: corresponding parts of congurent triangles are congurent. thats what i was taught. well i still have a question about HL, will the answer always be HL if its a right angle? or can i use a diffrent answer?

- April 23rd 2005, 11:12 PM #7Originally Posted by
**ticbol**

Conventions are OK if they are shared

If I say:

Please find the first KLH in the set Y that slorks up and down in ZTL metric without mishkining the HTG

I will__for sure__be ignored!

BTW, it's the first time in my career I hear the convention you are talking about.

After all we foreigner make the effort to write and read your language... you could kindly make the little effort to write down the problems in a clear way

PS

Even if I teach Math in Italian high schools since 1982, I'd never understood that cpctc means*corresponding parts of congruent triangles are congruent*

- April 23rd 2005, 11:57 PM #8