2. Lines and Angles

8 topics2 h

Chapter 2 of NCERT Mathematics for Class 6: Lines and Angles. Four sections — The basic objects, What an angle is, Measuring angles and Naming angles by their measure. Eight videos, 2 h in all.

Worked answers to the 50 exercise questions in this chapter →

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Part 1

The basic objects

9 minA point fixes a location; a segment is the shortest route between two pointsGeometry opens by naming two things nobody can draw. And the whole definition of a line segment hangs on one word: shortest.9 min · 11 partsहिंदी11 minLine and ray: what changes when you refuse to stopA line is a segment with the stopping taken away — and that one change is why two dots on a page decide an endless object completely.11 min · 11 partsहिंदी

Part 2

What an angle is

12 minAn angle is an amount of turn, not a pair of drawn armsThe two arms you can see are only the record of a turn that already happened — and once the size of an angle is the turn, cutting the arms shorter changes nothing at all.12 min · 12 partsहिंदी12 minComparing two angles without measuring either of themWhich of two angles is bigger can be settled completely before anyone owns a number — and the blank disc that settles it is one step short of a protractor.12 min · 12 partsहिंदी

Part 3

Measuring angles

12 minStraight and right angles as the landmarks of a full turnA right angle isn't “a corner that looks square”. It is exactly half a straight angle — and the word exactly is earned by folding paper, not by looking.12 min · 12 partsहिंदी13 minThe degree: why a full turn was cut into 360 equal partsA degree wasn't discovered — it was manufactured, by cutting one full turn into 360 equal slices. And 360 survived for an arithmetical reason you can check yourself in about a minute.13 min · 12 partsहिंदी15 minReading and drawing an angle with a protractorEvery protractor reading is a subtraction. Once you see that, the two rows of numbers stop being confusing and the six classic mistakes turn out to be one mistake with six faces.15 min · 12 partsहिंदी

Part 4

Naming angles by their measure

14 minAcute, obtuse and reflex: one classification covering every angleAcute, right, obtuse — most people stop there. The textbook doesn't: it asks whether every possible measure has been covered, and the answer is no. Half the range was still unnamed.14 min · 12 partsहिंदी

What you will be able to do

  • State what a point determines and what it does not have
  • Describe a line as a segment extended without end in both directions
  • State what two rays must share before they form an angle
  • Rank a set of drawn angles from smallest to largest by inspection, and say when inspection is not enough
  • Recognise a half turn as the angle whose arms lie in one straight line
  • Explain why comparison alone is not enough, and what assigning a number adds
  • Describe how a protractor's scale is built — a straight angle divided into 180 unit parts, with long marks every 10° and medium marks at each 5°
  • State the degree measures of a straight angle and a right angle

What this chapter assumes you already know

  • Recognising a straight edge from a curved one by eye
  • Reading a capital letter as a label rather than as a quantity
  • Comparing two paths and saying which is longer — no measurement required
  • The idea of extending a drawn stroke further in the same direction
  • The everyday sense of turning something about a fixed hinge
  • Comparing two lengths by placing one beside the other, from earlier work on measurement
  • The idea of half of something, from earlier work on fractions
  • Halving a quantity, and simple fractions of a whole

It builds directly on Mathematics is the search for patterns and for why they hold and Every number sequence is a rule, not a list.

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.

  • "A point is a very small dot."
  • "The line segment is the line I drew."
  • "Segment AB and segment BA are different because the letters differ."
  • "The end points are the boundary, so they are outside the segment."
  • "Labels are decoration."
  • "A line is a long segment."
  • "You could draw the whole line if you had a big enough sheet."
  • "Ray OA and ray AO are the same, because segment AB and segment BA are."