9. Symmetry

7 topics1 h

Chapter 9 of NCERT Mathematics for Class 6: Symmetry. Two sections — Lines of symmetry and Rotational symmetry. Seven videos, 1 h in all.

Worked answers to the 29 exercise questions in this chapter →

0 of 7 done — sign in to track this chapter

Part 1

Lines of symmetry

9 minA line of symmetry is a fold that makes the halves coincideA line of symmetry is not a line that looks central. It is a line you can fold along and find nothing sticking out.9 min · 12 partsहिंदी9 minWhy a figure can have several lines of symmetrySymmetry is a count, not a yes or no. Fold a square four different ways and every one of them works.9 min · 12 partsहिंदी9 minSymmetry as reflection: the fold line acts as a mirrorFolding paper is where it starts. Reflecting points is what lets you talk about figures too big to fold.9 min · 12 partsहिंदी10 minFold, blot, cut, punch: making a figure that is symmetric by constructionThe chapter changes direction here. Instead of hunting for symmetry, you make a shape that cannot help having it.10 min · 12 partsहिंदी

Part 2

Rotational symmetry

9 minAn angle of symmetry: turning a figure onto itselfA paper windmill has no line of symmetry anywhere. Search for one and you will not find it — and yet it is plainly symmetric.9 min · 12 partsहिंदी10 minCounting the angles of symmetry of polygons and radial-arm figuresHow many angles of symmetry does a figure get? Not the number of arms — that answer gets knocked down twice.10 min · 12 partsहिंदी10 minLine symmetry and rotational symmetry are independent of each otherFolding and turning are separate tests. A figure can pass either, both, or neither, and all four really happen.10 min · 12 partsहिंदी

What you will be able to do

  • State the fold test for a line of symmetry in one sentence, without using the word looks
  • Find every line of symmetry of a square by folding, and say how many there are
  • Restate the fold test as a statement about where each point goes
  • Explain why a fold made before a cut guarantees that the crease is a line of symmetry of the result
  • Give an example of a figure with no line of symmetry that still returns to itself under a turn
  • Count the angles of symmetry of a radial-arm figure and list them
  • State the two tests separately and say what each one measures

What this chapter assumes you already know

  • Recognising and naming ordinary plane shapes: triangle, square, rectangle, circle
  • The physical experience of folding a sheet of paper along a straight crease (Class 5 paper work is assumed by the chapter)
  • Knowing a square, a rectangle, a triangle and a hexagon by sight, and what a diagonal of a quadrilateral is
  • Class 5 paper folding and ink-blot work, which the chapter says the student has already done
  • Labelling the corners of a square with capital letters
  • Division with a remainder, and writing a quotient as a mixed fraction

It builds directly on A point fixes a location; a segment is the shortest route between two points, Line and ray: what changes when you refuse to stop, Shapes come in sequences too, with rules of their own, An angle is an amount of turn, not a pair of drawn arms, Straight and right angles as the landmarks of a full turn and The degree: why a full turn was cut into 360 equal parts.

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 line down the middle is a line of symmetry."
  • "Symmetric means it looks balanced or pretty."
  • "Lines of symmetry are vertical."
  • "Every figure has at least one line of symmetry."
  • "A line of symmetry has to be drawn on the figure to exist."
  • "Nearly overlapping is overlapping."
  • "If one diagonal is a line of symmetry, every diagonal is."
  • "A rectangle has four lines of symmetry, like a square."