Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Decide whether two triangles are similar
Geometry
CCSS HSG.SRT.A.2CCSS HSG.SRT.A.3England: GCSE Higher Geometry
Objective and success criteria
Students will: Decide whether two triangles are similar.
- 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: the next skill in this area.
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 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.
- Triangles ABC and DEF are similar. AB = 7 cm, BC = 4 cm and DE = 17.5 cm. Find EF in cm. → 10Prompt: Find the scale factor from the matching sides AB and DE.
- Two similar solids have a length scale factor of 4. The smaller has volume 4 cm³. What is the volume of the larger, in cm³? → 256Prompt: Volumes scale by the cube of the length scale factor.
- Triangles ABC and DEF are similar. AB = 9 cm, BC = 12 cm and DE = 13.5 cm. Find EF in cm. → 18Prompt: Find the scale factor from the matching sides AB and DE.
Hook · 5 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: Decide whether two triangles are similar. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Triangle P has sides 5, 7, 8 cm. Triangle Q has sides 14.5, 17.5, 20 cm. Are they similar?
- Step 1: 14.5 ÷ 5 = 2.9; 17.5 ÷ 7 = 2.5; 20 ÷ 8 = 2.5
- Step 2: No
- Answer: No
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Triangle P has sides 3, 4, 5 cm. Triangle Q has sides 9, 12, 15 cm. Are they similar? (Yes / No) → YesPrompt: Match the shortest with the shortest, and so on.
- Triangle 1 has angles 44° and 71°. Triangle 2 has angles 44° and 65°. Are the triangles similar? (Yes / No) → YesPrompt: Find the third angle of triangle 1.
You do: independent practice · 10 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Triangle P has sides 5, 7, 8 cm. Triangle Q has sides 7.5, 10.5, 12 cm. Are they similar? (Yes / No) → YesPrompt: Match the shortest with the shortest, and so on.
- Triangle 1 has angles 32° and 42°. Triangle 2 has angles 32° and 106°. Are the triangles similar? (Yes / No) → YesPrompt: Find the third angle of triangle 1.
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
- 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