Similar shapes

Similar Shapes

• ‘Similar shapes’ refer to shapes that have the same shape but not necessarily the same size. They have the same angles and their corresponding sides are in proportion.

Criteria for Similarity

• Two shapes are similar if:
  • Their corresponding angles are equal.
  • Their corresponding sides are in direct proportion.

Scale Factor

• The scale factor of two similar shapes is the ratio of the lengths of their corresponding sides.
  • For example, if the sides of one shape are 3 times longer than the sides of a similar shape, the scale factor is 3.
  • In the case where one shape is smaller than the other, the scale factor is a fraction - say if a rectangle is half the size of another rectangle, the scale factor is 0.5 or 1/2.

Properties of Similar Shapes

• If two shapes are similar:
  • Their perimeters will be in the same ratio as the ratio of corresponding sides.
  • Their areas will be in the ratio of the square of the ratio of corresponding sides.
  • Their volumes (for 3D shapes) will be in the ratio of the cube of the ratio of corresponding sides.

Similar Shaped Triangles

• In similar triangles, corresponding angles are equal and corresponding sides are in proportion.
  • If we know two or more corresponding sides are in proportion and the included angle is equal, the triangles are similar.
  • This is sometimes referred to as the Side-Angle-Side (SAS) rule for similar triangles.

Remember, understanding the concept of similar shapes and their properties is vital for solving geometry problems. Always check for similarity when you see proportional sides and equal angles in a problem. Keep practicing related questions to strengthen your understanding.