Angles and Parallel Lines

1Summary 重點摘要

Parallel lines cut by a transversal: corresponding, alternate, co-interior angles have rules.

2Vocabulary cards Vocabulary

3Step by step Steps

1. 1. Basics of anglesAn angle is formed by two rays sharing a common endpoint, measured in degrees. Memorise three special values: a right angle is 90°, a straight angle is 180° (angles on a straight line), and a full turn is 360°. Two rules follow immediately: adjacent angles on a straight line add to 180°, and all angles around a point add to 360°. Combined with the parallel-line properties, these solve most angle-chasing questions.
2. 2. Parallel lines and a transversalWhen two parallel lines (marked //, never meeting) are cut by a transversal, eight angles appear. They are far from random and obey three fixed rules: corresponding angles are equal, alternate angles are equal, and co-interior angles add to 180°. Crucially, these rules hold only for parallel lines — if the question never states the lines are parallel, none of them may be used.
3. 3. Corresponding angles (F shape)Corresponding angles occupy matching positions on the two parallel lines, forming an F shape with the transversal. Rule: when the lines are parallel, corresponding angles are equal — if one is 60°, so is its partner. To spot them, trace the F along the transversal, and in your working quote the reason, such as 'corresponding angles, AB//CD', which is the expected format in geometry answers.
4. 4. Alternate angles (Z shape)Alternate angles lie between the parallel lines on opposite sides of the transversal, tracing a Z (or backwards Z) shape. Rule: when the lines are parallel, alternate angles are equal — if one is 70°, its partner across the transversal is also 70°. Drawing the Z is the most reliable way to identify them; do not mistake the pair sitting inside the lines on the same side for alternate angles, for that pair adds up instead of matching.
5. 5. Co-interior angles (C shape)Co-interior angles also lie between the parallel lines but on the same side of the transversal, forming a C shape. Rule: when the lines are parallel, co-interior angles are supplementary — they add to 180°. For example, if one is 110°, the other is 180° − 110° = 70°. This is the only 'adding' rule among the three and the one most often confused with alternate angles; remember 'F and Z are equal, C adds up'.
6. 6. Vertically opposite angles and strategyWhen two straight lines cross, the facing pair are vertically opposite angles and are equal: if one is 50°, so is the one opposite, while adjacent angles on the line make 180°. Strategy for angle-chasing: use vertically opposite and straight-line angles first, then cross the gap between the parallel lines with the F, Z and C shapes. Quote a reason beside every step — this is the standard format for earning geometry marks in exams.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Corresponding (F): equal
• Alternate (Z): equal
• Co-interior (C): add to 180°
• Vertically opposite: equal
• These rules only for parallel lines