When a transversal crosses two parallel lines, special angle relationships are created. These are tested extensively at GCSE.
Core Concepts
Corresponding Angles (F-angles)
Same position at each intersection. Equal.
Alternate Angles (Z-angles)
Opposite sides of the transversal, between the parallels. Equal.
Co-interior Angles (C-angles / Allied)
Same side of the transversal, between the parallels. Sum to 180°.
Vertically Opposite Angles
Where two lines cross. Equal.
Strategy
- Identify the parallel lines and transversal.
- Determine the angle relationship (F, Z, or C).
- Apply the rule.
Worked Example: Example 1
Problem
Corresponding angles: if one is , the other is .
Solution
Worked Example: Example 2
Problem
Co-interior angles: if one is , the other is .
Solution
Worked Example: Example 3
Problem
Alternate angles with algebra: → .
Solution
Practice Problems
- Find the missing angle: corresponding angle is .
- Co-interior angle pair: one is . Find the other.
- Alternate angles: . Find .
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Key Takeaways
Corresponding (F): equal.
Alternate (Z): equal.
Co-interior (C): sum to 180°.
Look for F, Z, C shapes in the diagram.