Thinking AAA proves congruence
"The AAA Assumption"
The Mistake in Action
Two triangles have all three angles equal. Therefore they are congruent.
Wrong: ✓ Congruent (AAA)
Why It Happens
Students know that angles being equal is important and assume three equal angles is enough. They confuse the conditions for similarity with congruence.
The Fix
AAA proves SIMILARITY, not congruence!
If all angles are equal, the triangles are the same shape but could be different sizes.
Congruent means same shape AND same size. You need at least one side measurement:
- SSS (three sides)
- SAS (two sides and included angle)
- ASA (two angles and included side)
- RHS (right angle, hypotenuse, side)
AAA = Similar, not Congruent
Spot the Mistake
Can you identify where this student went wrong?
All three angles are equal
Therefore congruent (AAA)
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: