Similarity

Similarity

Similarity

What are similar shapes?

• Two shapes are similar if they have the same shape and their corresponding sides are in proportion

  • One shape is an enlargement of the other

• Similarity does not imply congruence

  • Two similar shapes could be different enlargements of each other

How do we prove that two triangles are similar?

• To show that two triangles are similar you need to show that their angles are the same

  • If the angles are the same then corresponding lengths of a triangle will automatically be in proportion

• You can use angle properties to identify equal angles

  • Look out for for isosceles triangles, vertically opposite angles and angles on parallel lines

• If a question asks you to prove two triangles are similar

  • For each pair of corresponding angles

    • State that they are of equal size

    • Give a reason for why they are equal 

How do we prove that two shapes are similar?

• To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion

  • Divide the length of one side by the length of the corresponding side on the other shape to find the scale factor 

• If the scale factor is the same for all corresponding sides, then the shapes are similar