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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? (isosceles / equilateral / scalene / right-angled) → equilateralPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  2. A triangle has no equal sides. What type of triangle is it? (equilateral / isosceles / scalene / right-angled) → scalenePrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  3. A triangle has one angle of 90°. What type of triangle is it? (equilateral / scalene / isosceles / right-angled) → right-angledPrompt: 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 two angles and the side between them are equal. Which condition is this? (SSS / SAS / RHS (HL) / ASA) → ASAPrompt: S stands for side, A for angle, R for right angle and H for hypotenuse.
  2. Two triangles have two sides and a non-included angle equal (SSA). Must they be congruent? (Yes / No) → NoPrompt: 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 are known to be congruent because two angles and the side between them are equal. Which condition is this? (SAS / SSS / ASA / RHS (HL)) → ASAPrompt: S stands for side, A for angle, R for right angle and H for hypotenuse.
  2. Two triangles have two sides and the included angle equal (SAS). Must they be congruent? (Yes / No) → YesPrompt: Could you draw two different triangles that both fit the description?

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

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Congruent triangles

Name

Date

Score/ 6

  1. Question 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?

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

  2. Question 2

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

    • A. Yes
    • B. No

  3. Question 3

    Two triangles have all three sides equal (SSS). 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. SAS
    • B. SSS
    • C. ASA
    • D. RHS (HL)

  5. Question 5

    Two triangles have only two pairs of sides equal. Must they be congruent?

    • A. Yes
    • B. No

  6. Question 6

    Two triangles have two angles and the included side equal (ASA). Must they be congruent?

    • A. Yes
    • B. No

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Answer key: Congruent triangles

  1. 1. D. RHS (HL)

  2. 2. A. Yes

  3. 3. A. Yes

  4. 4. A. SAS

  5. 5. B. No

  6. 6. A. Yes