Back to the lesson plan builder
Lesson length30 min45 min60 min
Questions🔀 New questions

Print the plan for yourself; the student sheet prints on its own page after it.

Math lesson plan · 9th grade (Year 10 in England) · 30 minutes

Congruent triangles

Geometry

CCSS HSG.CO.B.8CCSS HSG.SRT.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Objective and success criteria

Students will: Congruent triangles.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Classify triangles; angles in a triangle; Translations, reflections and rotations

Leads to: Choose the congruence test (SSS, SAS, ASA, AAS, RHS)

Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Classify triangles; angles in a triangle; Translations, reflections and rotations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A triangle has all three sides equal. What type of triangle is it? (equilateral / right-angled / scalene / isosceles) → equilateralPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  2. A triangle has one angle of 90°. What type of triangle is it? (scalene / equilateral / right-angled / isosceles) → right-angledPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  3. A triangle has exactly two sides equal. What type of triangle is it? (scalene / isosceles / equilateral / right-angled) → isoscelesPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.

Hook · 3 min

  • 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: Congruent triangles. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Two triangles are known to be congruent because two sides and the angle between them are equal. Which condition is this?
  • Step 1: SAS
  • Answer: SAS
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  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? (ASA / SSS / RHS (HL) / SAS) → RHS (HL)Prompt: S stands for side, A for angle, R for right angle and H for hypotenuse.
  2. Two triangles have two angles and the included side equal (ASA). Must they be congruent? (Yes / No) → YesPrompt: Could you draw two different triangles that both fit the description?

You do: independent practice · 7 min

  • 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.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. 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?
  2. 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? (ASA / SSS / SAS / RHS (HL)) → RHS (HL)Prompt: S stands for side, A for angle, R for right angle and H for hypotenuse.

Watch out for

  • Thinking a square turned on its corner is no longer a square.
  • Reading the wrong scale on a protractor.

Support and stretch

Support

  • Review first: Classify triangles; angles in a triangle.
  • Use concrete materials: rulers and protractors.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Choose the congruence test (SSS, SAS, ASA, AAS, RHS).
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Congruent triangles

Name

Date

Score/ 6

  1. Question 1

    Two triangles have two sides and a non-included angle equal (SSA). Must they be congruent?

    • A. Yes
    • B. No

  2. Question 2

    Two triangles are known to be congruent because all three pairs of sides are equal. Which condition is this?

    • A. ASA
    • B. RHS (HL)
    • C. SSS
    • D. SAS

  3. Question 3

    Two triangles have all three angles equal (AAA). Must they be congruent?

    • A. Yes
    • B. No

  4. Question 4

    Two triangles are known to be congruent because two sides and the angle between them are equal. Which condition is this?

    • A. ASA
    • B. RHS (HL)
    • C. SAS
    • D. SSS

  5. Question 5

    Two triangles are known to be congruent because two angles and the side between them are equal. Which condition is this?

    • A. SAS
    • B. SSS
    • C. ASA
    • D. RHS (HL)

  6. Question 6

    Two triangles have two sides and the included angle equal (SAS). Must they be congruent?

    • A. Yes
    • B. No

Free from eurekami.com

for the adult only

Answer key: Congruent triangles

  1. 1. B. No

  2. 2. C. SSS

  3. 3. B. No

  4. 4. C. SAS

  5. 5. C. ASA

  6. 6. A. Yes