Which of the following can not be used to prove two triangles are congruent?

(Select all that apply)

 a

ASS

 b

SAS

 c

SSS

 d

HL

 e

AAA

 f

ASA

 g

AAS

The options that **cannot** be used to prove two triangles are congruent are:

- **a) ASS** (Angle-Side-Side): This is not a valid method for proving triangle congruence. It’s often referred to as the “Donkey Theorem” because it does not guarantee congruence unless in special cases like right triangles (which is covered under the HL theorem).
  
- **e) AAA** (Angle-Angle-Angle): This only proves similarity, not congruence. AAA ensures that the triangles have the same shape but doesn't guarantee the same size.

The valid methods for proving congruence are:

- **b) SAS** (Side-Angle-Side)
- **c) SSS** (Side-Side-Side)
- **d) HL** (Hypotenuse-Leg for right triangles)
- **f) ASA** (Angle-Side-Angle)
- **g) AAS** (Angle-Angle-Side)

Would you like further details on why these methods work or have any other questions?

Here are 5 related questions:
1. How does the SSA condition sometimes work for right triangles?
2. Can AAA prove two triangles are congruent if they are right triangles?
3. Why does the HL theorem only apply to right triangles?
4. What are the common mistakes students make when using congruence theorems?
5. How is similarity different from congruence in triangle proofs?

**Tip**: When working with triangle congruence, always check if the conditions match one of the valid theorems to avoid mistakes!

Which of the following can not be used to prove two triangles are congruent?

(Select all that apply)

a) ASS
b) SAS
c) SSS
d) HL
e) AAA
f) ASA
g) AAS

Discover which methods can and cannot be used to prove triangle congruence. This problem explores key theorems such as SAS, SSS, HL, and explains why methods like AAA and ASS do not guarantee congruence. Ideal for students in Grades 8-10.

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