7. A Tale of Three Intersecting Lines

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Chapter 7 of NCERT Mathematics for Class 7: A Tale of Three Intersecting Lines. Three sections — Constructing from three sides, Constructing from sides and angles and Altitudes and classification. Seven videos, 1 h in all.

Worked answers to the 20 exercise questions in this chapter →

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Part 1

Constructing from three sides

9 minWhy a compass beats trial and error for building a triangleA compass is not a tidier ruler. That is the whole video.9 min · 12 partsहिंदी10 minThe triangle inequality: which three lengths can closeTry to build a triangle with sides 3, 4 and 8 and the two arcs sweep past each other without ever meeting.10 min · 12 partsहिंदी

Part 2

Constructing from sides and angles

9 minConstructing from two sides and the angle between themThree lengths can quarrel with each other. Two sides with the angle wedged between them never can.9 min · 12 partsहिंदी9 minConstructing from two angles and the side between themTwo sides with the angle between them can never fail. Two angles with the side between them can — and the reason is not the one you expect.9 min · 12 partsहिंदी9 minWhy the three angles of any triangle add to 180°Measuring a hundred triangles gives a hundred totals near 180° and never tells you why. One line does.9 min · 12 partsहिंदी

Part 3

Altitudes and classification

10 minWhat an altitude is, and how to construct oneLean a five-metre pole over and it stands 4.70 tall, then 4.10. It is still five metres of pole — height and length are different questions.10 min · 12 partsहिंदी10 minTwo independent ways to classify a triangle: by side and by angleSorting triangles by sides and sorting them by angles are not two halves of one list. They are two separate questions put to the same shape.10 min · 12 partsहिंदी

What you will be able to do

  • Name the three vertices, three sides and three angles of a labelled triangle, and write the triangle's name in any vertex order
  • Decide, for a given triple of lengths, whether a triangle with those sidelengths exists, and justify the decision without constructing it
  • Identify, in a labelled triangle, which angle is included between two named sides
  • Identify which side is included between two named angles of a triangle
  • Given two angles of a triangle, find the third by adding a parallel line and arguing, not by measuring
  • State what makes a segment an altitude of a triangle
  • Name the three side-based classes and state the condition for each

What this chapter assumes you already know

  • Measuring and drawing a segment of a stated length with a marked ruler
  • Class 6 Ganita Prakash, the chapter "Playing with Constructions": using a compass to place a point at a fixed distance from a given point
  • A circle as the set of points at a fixed distance from its centre, and the words centre and radius
  • Naming points with capital letters, and reading a labelled figure
  • A circle as the points at a fixed distance from a centre; radius; two circles drawn on the same picture
  • Comparing sums: deciding whether one number is less than, equal to, or greater than the total of two others
  • Reading a rough, not-to-scale diagram as a record of stated lengths
  • Drawing an angle of a stated size at a given point on a given ray, with a protractor

It builds directly on The four angles at a crossing: vertically opposite and linear pairs, Alternate angles, and interior angles that add to 180° and Perpendicular lines as the case where all four are equal.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "The compass is just a neater way of drawing."
  • "A triangle has to sit on its longest side / on a horizontal side."
  • "∆ABC and ∆BAC are different triangles."
  • "Two arcs always cross, so any three lengths work."
  • "Isosceles means exactly two equal sides, so an equilateral triangle is not isosceles."
  • "The dashed circle in the figure is part of the answer."
  • "You have to check all three comparisons."
  • "If the inequality holds, the triangle obviously exists."