Year 8 Interactive Maths - Second Edition

Angles associated with Parallel Lines

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 7

Use the information given in the diagram to find:

a.  u
b.  v
c.  w
d.  x
e.  y

Solution:

Key Terms

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