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Year 7 Interactive Maths - Second Edition

Parallel Lines

If two lines are in the same plane and do not intersect, then the lines are said to be parallel.

The lines AB and CD are parallel


Arrows are placed on the lines AB and CD to indicate that they are parallel.

A line that meets two or more parallel lines is called a transversal.  Line PQRS in the following diagram is a transversal.

PQRS is called the transversal


If two parallel lines are cut by a transversal as shown in the next diagram, we refer as follows to the angles formed:

  • z and x (or u and v) are alternate angles
  • x and y are corresponding angles
  • u and x (or z and v) are allied (or co-interior) angles
  • y and z are vertically opposite angles
Remember that:
  • Alternate angles are always equal.
  • Corresponding angles are always equal.
  • Allied (or co-interior) angles are supplementary.
  • Vertically opposite angles are always equal.

Example 9

Use the information given in the diagram to find:

a.  x
b.  y
c.  z
d.  u
e.  p


x = 130     {Alternate angles}

y = 26     {Vertically opposite angles}

z = 50     {Allied angles}

u = 50     {Alternate angles}

p = 25     {Corresponding angles}

Key Terms

parallel lines, transversal, alternate angles, corresponding angles, allied angles, co-interior angles, vertically opposite angles

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