Students build triangles from given parts and see that SSS, SAS, ASA, AAS and RHS fix one triangle while SSA can give two (AC9M8SP01, node 1).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 10 min · Investigate 10 min · Modify 10 min · Practise and Make 10 min
Do the Run board yourself first: try SSA with a short BC. Students need triangle classification and the angle sum (Year 7).
The one idea: a test is a set of parts that fixes the triangle, so any two triangles with those parts are congruent. The common mistake is treating SSA as SAS (Tom's mistake).
The board draws every triangle the parts allow: none, one, or two (only for SSA).
Wider: show two triangles formed by a rectangle's diagonal are congruent (it leads to the quadrilateral proofs in two lessons).
Where the angle is. Ask students to point to the angle and say which sides meet there before they name a test.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student calls SSA 'SAS'. | Is the angle between the two sides? | SAS needs the included angle. |
| A student says AAA proves congruence. | Could a bigger triangle have the same angles? | Equal angles mean similar; congruence needs a side too. |
| A student matches the wrong sides. | Which corners match? Read the letters in order. | △ABC ≡ △PQR: A with P, B with Q, C with R. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Find the range of BC (with AB = 6 and angle A = 40°) that gives no triangle, two triangles and one triangle. What is special at the boundaries?
Support: A card with the four tests drawn, the equal parts marked.
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Congruent triangles". The idea: Congruence conditions for triangles: I can Students identify and apply the four conditions for triangle congruence (SSS, SAS, AAS, RHS) and explain why each is sufficient. What understanding looks like: - States all four congruence conditions correctly. - Identifies which condition applies to a given pair of triangles. - Explains why SSA is not a valid congruence condition. Mistakes students often make here: - A student calls SSA 'SAS'. - A student says AAA proves congruence. - A student matches the wrong sides. How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Congruent triangles".
Two triangles have AB = PQ = 7 cm, BC = QR = 5 cm and angle B = angle Q = 60°. Are they congruent? Which test?
Yes, by SAS: angle B is between AB and BC.
This starts AC9M8SP01.
Where it leads: similar shapes (next lesson), proving quadrilateral properties, and congruence algorithms.