This chapter studies the relationships between lines on a plane. When two lines cross they intersect at a point and form four angles: adjacent angles form a linear pair that adds to \(180^\circ\), and opposite angles are vertically opposite and are always equal. If all four angles are equal, each is \(90^\circ\) and the lines are perpendicular. Lines on the same plane that never meet, however far extended, are parallel. The key tool is the transversal — a line crossing two others, forming eight angles. When a transversal cuts a pair of parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior (same-side interior) angles add to \(180^\circ\). Conversely, equality of corresponding angles is exactly what guarantees that two lines are parallel. You learn to spot, mark and reason about these angle relationships, to draw parallel lines using a ruler and set square or by paper folding, and to prove results rather than rely only on measurement.
Intersecting lines, linear pairs and vertically opposite anglesPerpendicular linesParallel linesTransversals and the eight anglesCorresponding, alternate and co-interior angles
Key terms
Intersecting lines
Two lines that meet at a single point on a plane.
Linear pair
Two adjacent angles formed by intersecting lines that add up to \(180^\circ\).
Vertically opposite angles
The pair of opposite angles formed by intersecting lines; they are always equal.
Perpendicular lines
Lines that intersect so that all four angles are \(90^\circ\).
Parallel lines
Lines on the same plane that never meet however far they are extended.
Transversal
A line that intersects two or more other lines, forming eight angles with a pair.
Corresponding angles
Angles in matching positions at the two intersections of a transversal; equal when the lines are parallel.
Alternate angles
Angles on opposite sides of the transversal between the lines; equal when the lines are parallel.
Extra questions & answers
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A linear pair of angles adds up to:
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