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

• 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, AB = DE, ∠B = ∠E. Which test proves they are congruent? (SSS / AAS / ASA / Not enough to prove congruence) → ASAPrompt: Count the sides (S) and angles (A) given, and notice their order.
2. Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SSS? (∠Q = ∠Y / RP = ZX / ∠P = ∠X / PQ = YZ) → RP = ZXPrompt: 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 6 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 ABC and DEF have: ∠C = ∠F = 90°, hypotenuse AB = DE, AC = DF. Which test proves they are congruent? (RHS (hypotenuse–leg) / ASA / SSS / SAS) → RHS (hypotenuse–leg)Prompt: Count the sides (S) and angles (A) given, and notice their order.
2. Triangles PQR and XYZ have ∠P = ∠X and ∠Q = ∠Y. Which extra fact would prove them congruent by ASA? (∠R = ∠Z / PQ = XY / RP = ZX / QR = YZ) → PQ = XYPrompt: Write the letters of the test in order around the triangle.

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