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Math lesson plan · 10th grade (Year 11 in England) · 30 minutes

Find missing lengths in similar triangles

Geometry

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

Objective and success criteria

Students will: Find missing lengths in similar 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: Similar shapes

Leads to: Use length, area and volume scale factors

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 (Similar shapes). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Triangles ABC and DEF are similar. AB = 9 cm, BC = 4 cm and DE = 18 cm. Find EF in cm. → 8Prompt: Find the scale factor from the matching sides AB and DE.
  2. Two similar solids have a length scale factor of 4. The smaller has volume 13 cm³. What is the volume of the larger, in cm³? → 832Prompt: Volumes scale by the cube of the length scale factor.
  3. Triangles ABC and DEF are similar. AB = 5 cm, BC = 12 cm and DE = 12.5 cm. Find EF in cm. → 30Prompt: Find the scale factor from the matching sides AB and DE.

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: Find missing lengths in similar 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: Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 7 cm, PQ = 28 cm and BC = 10 cm. Find QR.
  • Step 1: k = 28 ÷ 7 = 4
  • Step 2: QR = 10 × 4 = 40 cm
  • Answer: 40
  • 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. Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 5 cm, PQ = 10 cm and BC = 8 cm. Find QR. → 16Prompt: Find the scale factor from the matching pair you know.
  2. In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 8 cm, DB = 2 cm and DE = 7 cm. Find BC to 1 decimal place. → 8.8Prompt: Triangles ADE and ABC are similar (corresponding angles).

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. In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 3 cm, DB = 10 cm and DE = 8 cm. Find BC to 1 decimal place. → 34.7Prompt: Triangles ADE and ABC are similar (corresponding angles).
  2. Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 5 cm, PQ = 12.5 cm and BC = 12 cm. Find QR. → 30Prompt: Find the scale factor from the matching pair you know.

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: Similar shapes.
  • 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: Use length, area and volume scale factors.
  • 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-10.

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

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Find missing lengths in similar triangles

Name

Date

Score/ 6

  1. Question 1

    Zara is 1.2 m tall and casts a 1.2 m shadow. At the same moment a tree casts a 30 m shadow. How tall is the tree, to 1 decimal place?

    Answer

  2. Question 2

    In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 7 cm, DB = 4 cm and DE = 4 cm. Find BC to 1 decimal place.

    Answer

  3. Question 3

    Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 4 cm, PQ = 8 cm and BC = 3 cm. Find QR.

    Answer

  4. Question 4

    Maya is 1.2 m tall and casts a 3 m shadow. At the same moment a tree casts a 21 m shadow. How tall is the tree, to 1 decimal place?

    Answer

  5. Question 5

    In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 8 cm, DB = 7 cm and DE = 4 cm. Find BC to 1 decimal place.

    Answer

  6. Question 6

    Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 9 cm, PQ = 18 cm and BC = 10 cm. Find QR.

    Answer

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Answer key: Find missing lengths in similar triangles

  1. 1. 30

  2. 2. 6.3

  3. 3. 6

  4. 4. 8.4

  5. 5. 7.5

  6. 6. 20