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Grade 7/ Maths/ Parallel & Intersecting Lines
Chapter 5 · NCERT Ganita Prakash

Parallel and
Intersecting Lines

Some lines cross; others run side by side forever and never touch. Once you know which angles are equal and which add to 180°, you can find a missing angle without ever measuring it.

📐 3 topics⏱ ~22 min📝 12-question quiz
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Play with it

Explore angle relationships

When lines cross — or when a transversal cuts across two parallel lines — the angles follow simple rules. Tap each relationship to see what its angles do.

Explore · Angles made by linestap a relationship

Learn

The three big ideas

Two straight lines on a flat page can do one of two things:

  • Intersecting lines cross each other and meet at exactly one point (the point of intersection).
  • Parallel lines never meet, however far you extend them, and stay the same distance apart — written as PQ ∥ RS.
  • Perpendicular lines are a special case of intersecting lines: they cross at 90°.

Use the explorer above to meet the angles these lines make.

When two lines cross they make four angles. Two rules cover them all:

  • Vertically opposite angles — the pair directly across the crossing point — are EQUAL.
  • A linear pair — two adjacent angles sitting on a straight line — adds up to 180°.

Worked example. Two lines cross and one angle is 110°. Find (a) the angle vertically opposite it, and (b) its linear-pair neighbour.

(a) Vertically opposite angles are equal, so the opposite angle is also 110°.
(b) A linear pair on a straight line adds to 180°, so the neighbour is 180 − 110 = 70°.

A transversal is a line that crosses two (or more) other lines. When the two lines are parallel, the angles line up beautifully:

  • Corresponding angles (matching corners, the F-shape) are EQUAL.
  • Alternate interior angles (the Z-shape pair between the lines) are EQUAL.
  • Co-interior / allied angles (the C-shape pair, same side, between the lines) ADD UP TO 180°.
Common mistake: alternate interior angles are EQUAL, but co-interior (allied) angles are SUPPLEMENTARY — they add up to 180°. Do not swap the two rules: never make co-interior angles "equal" or alternate angles "add to 180°".

Where you'll meet it

Lines & angles in the real world

Railway tracks & ruled paper

The two rails of a railway track are parallel — always the same distance apart so the wheels never jam. The blue lines on your notebook are parallel too, keeping your handwriting straight across the page.

Road junctions & design

Where roads cross they form intersecting lines, and a connecting road acts like a transversal. Planners, tile-layers and builders use vertically opposite and corresponding angles to set out junctions and patterns accurately.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

Score 0/12

Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 7 Maths textbook, Ganita Prakash (ncert.nic.in).

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