Unit 3 · Geometry and Measurement · Lesson Three
Parallelism
When a transversal crosses two straight lines it creates eight angles. This guide explains every pair, shows what changes when the two lines are parallel, and trains you to write proofs that hold up.
Lines m ∥ n cut by transversal t: ∠1 and ∠5 are corresponding angles.
Learning outcomes
- 01Understand the concept of parallelism.
- 02Identify the angles formed when a straight line intersects two other straight lines.
- 03Recognise corresponding angles.
- 04Recognise alternating (alternate) angles.
- 05Recognise interior angles on the same side of a transversal.
- 06Relate the angles formed when a transversal cuts two parallel lines.
- 07Prove that two straight lines are parallel.
- 08Write a clear geometric proof.
Vocabulary
- Parallelism
- Two coplanar straight lines that never meet, however far they extend.
- Transversal
- A straight line that cuts two or more straight lines at two different points.
- Corresponding angles
- Same side of the transversal, one interior and one exterior, not adjacent.
- Alternating angles
- On opposite sides of the transversal, not adjacent — both interior or both exterior.
- Interior angles (same side)
- Two interior angles lying on the same side of the transversal.
Lesson map
01Pairs of angles formed by a transversalInterior, exterior, corresponding, alternating and co-interior angles.02The relation when the two lines are parallelEqual in measure or supplementary — with worked examples.03Proving two lines are parallel & writing proofsThe three conditions, plus a six-step method for a clean proof.04Exercise 13 — graded questionsComplete, find x, true/false and multiple-choice questions.05Activities, drills & learning gamesAngle hunter, proof builder, timed challenge and a parallel-line lab.