GCSE Maths - Similar Shapes #104

Introduction

This tutorial will guide you through the concept of similar shapes and how to use scale factors to find missing lengths of sides. Understanding similar shapes is essential for various applications in geometry, making this knowledge valuable for students preparing for their GCSE Maths exams.

Step 1: Understanding Similar Shapes

• Similar shapes are figures that have the same shape but not necessarily the same size.
• They maintain proportional dimensions, meaning the ratios of corresponding sides are equal.
• To determine if two shapes are similar, check:
  • Corresponding angles are equal.
  • The ratio of the lengths of corresponding sides is constant.

Step 2: Identifying Scale Factors

• A scale factor is the ratio of the length of a side of one shape to the length of the corresponding side of another shape.

• To find the scale factor:

  • Select one side from each shape.
  • Divide the length of the side from the larger shape by the length of the corresponding side from the smaller shape.

  Example:

  • If Shape A has a side length of 8 cm and Shape B (similar shape) has a side length of 4 cm, the scale factor is:

  Scale Factor = Length of Shape A / Length of Shape B
                = 8 cm / 4 cm
                = 2
  

Step 3: Finding Missing Lengths Using Scale Factors

• When given a similar shape with one side length missing, you can use the scale factor to find it.

• Use the following steps:

  1. Identify the known dimensions of both shapes.
  2. Calculate the scale factor using the known dimensions.
  3. Set up a proportion to solve for the missing side.

  Example:

  • If you know one side of Shape B is 5 cm and the scale factor is 2, the corresponding side in Shape A can be found as follows:

  Side in Shape A = Side in Shape B × Scale Factor
                   = 5 cm × 2
                   = 10 cm
  

Step 4: Practice Problems

• To reinforce your understanding, try solving the following problems:

  1. If Shape X has a side of 12 cm and Shape Y is similar with a side of 6 cm, what is the scale factor?
  2. If a side of Shape C is 3 cm and the scale factor to Shape D is 4, what is the length of the corresponding side in Shape D?

• Check your answers:

  1. Scale factor = 12 cm / 6 cm = 2
  2. Side in Shape D = 3 cm × 4 = 12 cm

Conclusion

Understanding similar shapes and scale factors is crucial in geometry. Remember that similar shapes have proportional sides and equal angles. Practice calculating scale factors and finding missing lengths to solidify your skills. As a next step, explore more complex problems involving area and volume of similar shapes to further your understanding.