Similar Shapes and Scale Factors
This lesson introduces students to the concept of geometric similarity. Students will learn that similar shapes have equal corresponding angles and sides in the same proportion. The lesson focuses on identifying scale factors and applying them to find unknown dimensions in 2D shapes.
Learning objectives
- Identify the difference between congruent and similar shapes.
- Calculate the linear scale factor between two similar shapes.
- Find missing side lengths in similar shapes using the scale factor.
- Understand the relationship between length scale factors and area scale factors (Stretch).
Lesson plan (60 minutes)
Introduction · 5 min
Starter: Review of simplifying ratios and solving basic linear equations (e.g., 2x = 10).
Instruction · 10 min
Teacher explanation: Define similarity vs congruence. Demonstrate how to find the scale factor using corresponding sides.
Instruction · 5 min
Worked Example: Step-by-step calculation of a missing side length on the whiteboard.
Guided Practice · 25 min
Differentiated Worksheet Activity: Students work through Support, Core, or Stretch tasks.
Transition · 5 min
Mini-plenary: Discussion on area scale factors (introduction to Stretch concepts).
Assessment · 10 min
End of lesson Quiz: Multiple choice assessment.
Key vocabulary
- Congruent
- Shapes that are exactly the same shape and size.
- Similar
- Shapes that are the same shape but different sizes; their sides are in proportion.
- Scale Factor
- The number a length is multiplied by to create a similar shape.
- Corresponding Sides
- Sides that are in the same relative position in two similar shapes.
- Ratio
- A mathematical comparison between two numbers, showing how many times one contains the other.
Core worksheet (first questions)
- A photo is 10cm wide. It is enlarged to be 15cm wide. What is the scale factor?
- Triangle A (side 8cm) is similar to Triangle B. The scale factor is 1.5. Calculate the side of B.
- Rectangle M is 15cm long and 9cm wide. Similar Rectangle N is 10cm long. Calculate the width of N.
- Two similar pentagons have sides of 5cm and 7.5cm. If the smaller one has another side of 5cm, what is the matching side on the larger one?
Quiz (sample)
1. What defines 'similar' shapes in geometry?
- A. Shapes that are identical in every way
- B. Shapes that have the same area
- C. Shapes that are the same shape but different sizes
- D. Shapes with the same number of sides
2. What is true about the corresponding angles in two similar shapes?
- A. They are equal
- B. They are doubled
- C. They are in the same ratio as the sides
- D. They add up to 180 degrees
3. If a side of 4cm on Shape A corresponds to a side of 12cm on Shape B, what is the scale factor from A to B?
- A. 2
- B. 3
- C. 6
- D. 9
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