Geometric Twins

Overview

Geometric Twins is about figures that match each other through symmetry and congruence. We learn when two shapes are identical and how symmetry appears in shapes around us.

Key concepts

• Line (reflection) symmetry: one half is the mirror image of the other.
• Rotational symmetry: a shape looks the same after a turn.
• Congruent figures have the same shape and size.
• Order of rotational symmetry counts matches in one full turn.

Important formulae

• Angle of rotation = 360° ÷ order of symmetry
• Congruent figures: corresponding sides and angles are equal
• A square has 4 lines of symmetry and order 4

Solved example

1. Find the angle of rotation for a shape with rotational symmetry of order 3.
2. Angle = 360° ÷ order.
3. Angle = 360° ÷ 3 = 120°.

Important questions

1. How many lines of symmetry does an equilateral triangle have?
2. What is the order of rotational symmetry of a rectangle?
3. Are two squares of side 4 cm congruent?
4. Name a letter of the alphabet with both line and rotational symmetry.

Quick revision

Line symmetry folds a figure onto itself; rotational symmetry turns it onto itself. Congruent figures are exact copies with equal sides and angles.