Parallel and Intersecting Lines — Class 7 Mathematics

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 , and opposite angles are vertically opposite and are always equal. If all four angles are equal, each is 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 . 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.