Similar Shapes

Understanding Similar Shapes

• Define similar shapes as shapes that have the exact same shape but may be a different size.

• Understand that if two shapes are similar, they can be transformed into one another through enlargements only, where all lengths are multiplied by the same scale factor.

• Comprehend that scale factor enlargements change the size but not the shape of the figure. Hence, ratios of corresponding side lengths remain the same.

• Realise that corresponding angles in similar shapes are equal. This is due to equal ratios of corresponding sides maintaining the shape, causing no change in the angles.

Criteria for Similarity

• Understand three main similarity rules: Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Angle (AA).

• Recall the Side-Side-Side (SSS) similarity rule: If the ratios of all corresponding sides in two shapes are equal, then the shapes are similar.

• Understand the Side-Angle-Side (SAS) similarity rule: If the ratios of two corresponding sides in two shapes are equal and the included angle is the same in both shapes, then the shapes are similar.

• Comprehend the Angle-Angle (AA) similarity rule: If two corresponding angles in two shapes are equal, then the shapes are similar.

Applying Similarity Concepts

• Recognize that two similar shapes have the same area ratio as the square of their linear (side-length) scale factor.

• Understand that two similar shapes have the same volume ratio as the cube of their linear (side-length) scale factor.

• Apply similarity rules to determine similarity in various geometric shapes and figures.

• Use similar shapes to solve geometric problems and real-life application problems.

• Solve problems involving similarity in triangles and other polygons.

• Appreciate that similar shapes can have different orientations in space. Similarity doesn’t involve position or orientation, only size and shape.