Schooling · Class 7 · Mathematics · Parallel and Intersecting Lines · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash
Parallel and Intersecting Lines: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Two lines on a flat surface are…
- Two lines that cross each other at…
- When two lines intersect, they form…
- A transversal is a line that cuts…
- When a transversal crosses two…
- Corresponding angles are in the same…
- Alternate angles are on opposite…
- Formulas and facts
- Vertically opposite angles are equal
- If two parallel lines are cut by a…
- If a transversal makes equal…
- Watch out for
- Confusing alternate angles with…
- Thinking vertically opposite angles…
- Forgetting that angle rules for…
- Adding alternate angles instead of…
What this chapter is about
This chapter helps you understand how lines behave when they are drawn on a flat surface. You will learn about lines that cross each other (intersecting lines) and lines that never meet no matter how far you extend them (parallel lines).
Key ideas
- Two lines on a flat surface are called parallel lines if they never meet, even when extended forever. We write AB ∥ CD to say line AB is parallel to line CD.
- Two lines that cross each other at exactly one point are called intersecting lines. The point where they meet is called the point of intersection.
- When two lines intersect, they form four angles. The angles opposite to each other are called vertically opposite angles, and they are always equal.
- A transversal is a line that cuts across two or more lines at different points.
- When a transversal crosses two parallel lines, it creates eight angles. Some special pairs of these angles are equal, and some add up to 180°.
- Corresponding angles are in the same position at each intersection point. When the two lines are parallel, corresponding angles are equal.
- Alternate angles are on opposite sides of the transversal and between the parallel lines. When the two lines are parallel, alternate angles are equal.
- Co-interior angles (also called same-side interior angles) are on the same side of the transversal and between the parallel lines. When the two lines are parallel, they add up to 180°.
Formulas and facts to remember
- Vertically opposite angles are equal.
- If two parallel lines are cut by a transversal: corresponding angles are equal.
- If two parallel lines are cut by a transversal: alternate interior angles are equal.
- If two parallel lines are cut by a transversal: co-interior angles add up to 180°.
- If a transversal makes equal corresponding angles (or equal alternate angles) with two lines, then those two lines are parallel.
Common mistakes
- Confusing alternate angles with corresponding angles → Draw the transversal and mark positions carefully; alternate angles are on opposite sides.
- Thinking vertically opposite angles add up to 180° → They are equal, not supplementary.
- Forgetting that angle rules for parallel lines do not work if the lines are not parallel → Always check whether the lines are truly parallel before using the rules.
- Adding alternate angles instead of recognising they are equal → Remember: alternate angles are equal; co-interior angles add to 180°.
Quick revision
- Parallel lines never meet; intersecting lines meet at one point.
- Vertically opposite angles are equal.
- When a transversal cuts parallel lines, corresponding angles are equal and alternate angles are equal.
- Co-interior angles between parallel lines add up to 180°.
- To prove lines are parallel, show that corresponding or alternate angles are equal.