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Grade 7/ Maths/ Three Intersecting Lines
Chapter 7 · NCERT Ganita Prakash

A Tale of Three
Intersecting Lines

Three lines meet and trap a triangle. Bend two of its corners however you like — the three angles still add up to exactly 180°, every single time.

📐 3 topics⏱ ~23 min📝 12-question quiz
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Play with it

Bend the triangle

Drag the two sliders to change angles A and B. The third angle C adjusts itself — because the three angles must always total 180°.

Explore · Angle-sum of a triangledrag A and B

Learn

The three big ideas

When three straight lines cross each other (and aren't all parallel), they enclose a triangle — three vertices (corners), three sides, and three interior angles.

No matter the shape, the three interior angles of a triangle always add up to 180°. So if you know two angles, you can find the third by subtracting from 180.

Worked example. Two angles of a triangle are 50° and 60°. Find the third.

Third angle = 180 − (50 + 60) = 180 − 110 = 70°. Check it on the slider above!

Common mistake: thinking the angles add to 360°. That's a full turn (or a quadrilateral). For a triangle it's 180°.
  • Acute-angled — all three angles less than 90°.
  • Right-angled — one angle exactly 90°.
  • Obtuse-angled — one angle more than 90° (only one is possible).

An exterior angle of a triangle equals the sum of the two interior angles opposite to it.

Where you'll meet it

Triangles hold the world up

Strong by shape

Triangles don't bend out of shape under load, so bridges, roof trusses and cranes are built from them. The angle-sum rule lets engineers find a missing angle exactly.

Maps & navigation

Surveyors and sailors use triangles (triangulation) to fix positions and distances — knowing two angles gives the third and unlocks the rest.

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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