Parallel lines

Parallel lines

Introduction

• Parallel lines are a central concept in geometry, an important part of the mathematical discipline of algebra.
• They are lines in a plane that do not meet; that is, they remain the same distance apart over their entire length.
• Parallelism has important consequences in the study of properties of shapes in geometry.

Identifying Parallel lines

• We use the symbol ‘

  ’ to indicate that two lines are parallel. For example, if we have two lines ‘a’ and ‘b’, we write ‘a

  b’ to mean that ‘a’ is parallel to ‘b’.

• In diagrams, parallel lines are often marked with the same number of arrows.
• If two lines are cut by a transversal, the corresponding angles are equal. This property is constantly used for identifying parallel lines in algebra.

Properties of Parallel Lines

• Parallel lines establish several important properties in geometry. The angles they form when intersected by a third line, a transversal, are particularly noteworthy.
• Alternate angles formed between parallel lines are equal. Alternate angles are the pairs of angles on opposite sides of the transversal but outside the parallel lines.
• Corresponding angles between parallel lines are also equal. Corresponding angles are the angles that occupy the same relative position at each intersection where a straight line crosses two others.
• Co-interior angles between parallel lines add up to 180°. These are the angles on the same side of the transversal and inside the parallel lines.

Applications of Parallel lines

• An understanding of parallel lines is essential to understanding the properties of many geometric figures such as squares, rectangles, parallelograms, and more complex polygons.
• The discovery of parallel lines properties has significant implications in real-world tasks such as road construction, architectural design, and urban planning.

Key Points

• Recognising the properties of parallel lines and their angles is a vital skill in algebra and geometry.
• To become comfortable with parallel lines, practice identifying them in various geometric figures and ensure you understand the concept of transversals, corresponding angles, alternate angles, and co-interior angles.
• Make sure to review and practice problems involving parallel lines, positioning them at different angles, and including other geometric properties.