Question

Which of the following are not congruence theorems for right triangles? Check all that apply.

Answer 1

A. LA
B. HL
C. AA
D. HA
E. HH
F. LL

Answer 2

Translate from Right to more general

LL ==> SAS - Congruence
HH -- Doesn't make sense.
HA ==> AAS - Is that one or not?
AA ==> AAA - Nope, That's similarity.
HL ==> You do the last two.
LA ==> Well?

Answer 3

HL = SSS
LA = ASA

Answer 4

Not quite:

HL ==> SSA It gives two sides and we know the non-included angle. This MAY be a problem, and is normally considered at risk for being the "Ambiguous Case", but does a right triangle solve this problem?

LA ==> ASA -- THERE is a congruence.

Answer 5

So which congruence theorems do not work for right triangles

Answer 6

They're all catalogued above. Reason it out and pick the right ones.

Answer 7

HH
AA
HL do not work

Answer 8

How about HA?

Answer 9

I dont think it is a congruence theorem so that dosent work eithier

Answer 10

am i right? @tkhunny

Answer 11

Sorry, both HA and HL work for RIGHT triangles.

HA ==> AAS and this is a general congruence theorem


HL ==> SSA. This is NOT a general congruence theorem. However, the Pythagorean theorem tells us that we do know the length of the third side, so really:

For RIGHT triangles.
HL ==> SSA ==> SSS and it IS a congruence.

I'm going to guess your entire class will miss this one.

Answer 12

So HL
and HA work for right triangles but what does not work

Answer 13

Is AA the only theorem that does not work

Answer 14

And HH - since that doesn't actually exist.

Answer 15

So AA and HH are the only 2 that are NOT congruence theorems for right triangles

Answer 16

Do you still doubt? We discussed them all. Did we rule out any others or did we rule them in?

Answer 17

im just double checking

Answer 18

I'm going to make you tell me. We can go through the list again or you can proceed with confidence. What's it going to be? :-)