Parallel Lines

• Parallel lines run alongside each other at an equal distance apart and never intersect.
• On a plane, two lines are parallel if they have the same gradient.

• The symbol for parallel lines is ‘

  ’, for example, if we have two lines ‘a’ and ‘b’, we say ‘a

  b’ which means ‘line a is parallel to line b’.

• When a transversal intersects two or more parallel lines, corresponding angles are equal. This means that the angles that occupy the same relative position at each intersection where the straight line crosses the two others.
• The alternate angles (also known as Z-angles) between two parallel lines cut by a transversal are equal. These are angles formed when a straight line crosses two parallel lines and the angles that are formed on opposite sides of the transversal and inside the parallel lines.
• The sum of the interior angles on the same side of the transversal is 180 degrees - these are called ‘co-interior’ or ‘allied’ angles.
• The exterior angle of a triangle is equal to the sum of the two interior opposite angles. This concept is frequently illustrated in problems involving parallel lines.
• We also use parallel lines when understanding the properties of polygons - for example, opposite sides of a parallelogram are equal and parallel.
• A trapezium is a four-sided figure with one pair of parallel lines.
• Parallel lines are used in real-world applications too, such as railway tracks, edges of a notebook, sides of a road, etc.