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Year 9 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.


Note:

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.



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

Recall 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 6

Use the information given in the diagram to find:

a.  x
b.  y
c.  z
d.  u
e.  p

Solution:


Key Terms

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

 


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