Today is rung 6 of 6 on this topic
Triangle congruence and similarity
Can do: Applies the congruence and similarity criteria correctly and knows why SSA fails.
Why it matters
It's the toolkit for most geometric proof, and the criteria are memorised without understanding more often than not.
What it looks like when it's wobbly
Uses SSA as if it were a criterion and can't say why the exceptions exist.
⏱️ Two-minute check
"Which criteria prove congruence? Why isn't SSA one of them?"
Solid looks like: SSS, SAS, ASA, AAS, HL — and can describe or draw the SSA ambiguity.
The full activity for this topic · 30 minutes
Build the Ambiguous Case
- 1Build triangles from given measurements and see which sets force a unique triangle.
- 2Try SSA and physically construct two different triangles from the same data.
- 3That construction is the reason the criterion doesn't exist — no memorisation needed.
- 4Use similarity to find a real height by shadow or by a mirror on the ground.
- 5Write one proof using each criterion.
If it's too hard
Identify which criterion applies to given diagrams.
If it's too easy
Proofs requiring two triangles and an intermediate result.
Say this
"Build it with the straws. Can you make two different triangles from that data? Then it can't be a rule."