Chapter 5: Parallel and Intersecting Lines
Lines that cross make angles with fixed relationships, and lines that never meet are special too. In this chapter we find angles at crossings without measuring, learn what parallel lines are, use a transversal to test for them, draw them with a set square, and solve angle puzzles with alternate and interior angles.
In this chapter you will
- use linear pairs and vertically opposite angles
- recognise parallel and perpendicular lines
- use corresponding angles to test for parallel lines
- draw parallel lines and find angles with alternate and interior angles
Topics
- Across the Line and Perpendicular Lines NCERT 5.1–5.2
Two crossing lines make 4 angles: a linear pair adds to 180°, vertically opposite angles are equal.
- Between Lines NCERT 5.3–5.4
Parallel lines: same plane, never meet, always the same distance apart.
- Transversals and Corresponding Angles NCERT 5.5–5.6
A transversal makes 8 angles; corresponding angles sit in the same position at each crossing.
- Drawing Parallel Lines NCERT 5.7
A set square slid along a ruler draws parallel lines: the corresponding angles stay equal.
- Alternate Angles NCERT 5.8–5.9
With parallel lines, alternate angles are equal (∠3 = ∠5, ∠4 = ∠6).
Key words
- Linear pair
- two angles side by side on a line; they add up to 180°
- Vertically opposite angles
- opposite angles where two lines cross; always equal
- Perpendicular
- lines that meet at 90°
- Parallel lines
- lines in one plane that never meet
- Transversal
- a line crossing two other lines
- Corresponding angles
- angles in the same position at the two crossings
- Alternate angles
- angles between the lines on opposite sides of the transversal
Summary
- Crossing lines: linear pairs add up to 180°, vertically opposite angles are equal.
- Parallel lines lie in one plane and never meet; perpendicular lines meet at 90°.
- A transversal makes 8 angles; corresponding angles are equal exactly when the lines are parallel.
- With parallel lines, alternate angles are equal and same-side interior angles add up to 180°.