• Quick retrieval from earlier learning (Congruent triangles). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Two triangles are known to be congruent because two sides and the angle between them are equal. Which condition is this? (ASA / RHS (HL) / SAS / SSS) → SASPrompt: S stands for side, A for angle, R for right angle and H for hypotenuse.
2. Two triangles have all three angles equal (AAA). Must they be congruent? (Yes / No) → NoPrompt: Could you draw two different triangles that both fit the description?
3. Two triangles are known to be congruent because both have a right angle, and the hypotenuses and one other side are equal. Which condition is this? (RHS (HL) / SSS / ASA / SAS) → RHS (HL)Prompt: S stands for side, A for angle, R for right angle and H for hypotenuse.

• Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
• Share the objective: Choose the congruence test (SSS, SAS, ASA, AAS, RHS). Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Triangles ABC and DEF have: ∠A = ∠D, AB = DE, ∠B = ∠E. Which test proves they are congruent?
• Step 1: ASA
• Answer: ASA
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, BC = EF. Which test proves they are congruent? (AAS / ASA / RHS (hypotenuse–leg) / SSS) → AASPrompt: Count the sides (S) and angles (A) given, and notice their order.
2. Triangles KLM and STU have ∠K = ∠S and ∠L = ∠T. Which extra fact would prove them congruent by ASA? (KL = ST / LM = TU / MK = US / ∠M = ∠U) → KL = STPrompt: Write the letters of the test in order around the triangle.

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. Triangles KLM and STU have ∠K = ∠S and ∠L = ∠T. Which extra fact would prove them congruent by ASA? (LM = TU / ∠M = ∠U / MK = US / KL = ST) → KL = STPrompt: Write the letters of the test in order around the triangle.
2. Triangles ABC and DEF have: AB = DE, ∠B = ∠E, BC = EF. Which test proves they are congruent? (AAS / SAS / RHS (hypotenuse–leg) / SSS) → SASPrompt: Count the sides (S) and angles (A) given, and notice their order.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.