Three guided lessons with explanations, visual steps, practice and a final check.
Original chapter companion covering line symmetry, grid reflections and symmetry counts for familiar shapes. It does not reproduce or solve every textbook exercise.
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LESSON 1
Test a mirror line
Explain line symmetry using a fold or reflection.
A line of symmetry divides a shape into matching mirror halves.
Look at the whole shape
Start with a rectangle whose length is greater than its width.
Try a fold
Fold along the vertical line through its centre.
Match the points
Each point on one side has a matching point the same distance from the line on the other side.
Check the full shape
Every edge and point must match. This vertical centre line is a line of symmetry.
Worked example: A non-square rectangle has a vertical and a horizontal line of symmetry. Fold along either centre line: matching edges meet. A slanting diagonal is not a symmetry line.
Watch for this: Two parts with the same area are not enough. A diagonal divides a non-square rectangle into equal-area triangles, but they do not match by folding along that diagonal.
Discuss: Cut a paper rectangle with unequal adjacent sides. Test its two centre folds and one diagonal fold.
LESSON 2
Complete a reflected pattern
Place a reflected point on the same row and at equal distance from a vertical mirror.
For a vertical mirror, a point moves across the line while staying at the same height.
Find the original point
Point A is two grid spaces left of the vertical mirror.
Measure to the mirror
Count horizontally from A to the mirror: two spaces.
Copy the distance
Count two spaces to the right on the same row and place the image point.
Check a matching pair
The mirror lies halfway between the two points. Each is two spaces from it.
Worked example: A point is 3 grid spaces to the right of a vertical mirror. Its image is 3 spaces to the left on the same row. The two points are 6 spaces apart.
Watch for this: Reflecting is not copying a point to any nearby place. Keep equal perpendicular distance and the same row for a vertical mirror.
Discuss: Draw a vertical line on squared paper. Place three points on the left and reflect them one at a time.
LESSON 3
Count symmetry lines
Find all symmetry lines of familiar regular and non-regular shapes.
Test each proposed line by matching the entire shape, and count each distinct line once.
Try the vertical centre line
A square matches across its vertical centre line. That is one symmetry line.
Try the horizontal centre line
Its horizontal centre line also works. There are now two.
Test one diagonal
A square has equal sides, so this diagonal fold also matches. This is the third line.
Test the other diagonal
The other diagonal works too. These four are all the symmetry lines of a square.
Worked example: An equilateral triangle has 3 symmetry lines, each joining a vertex to the midpoint of the opposite side. A non-square rectangle has 2, and a square has 4.
Watch for this: A square has four symmetry lines; a non-square rectangle has only two. Do not give every rectangle the square’s diagonal symmetry.
Discuss: Draw a square, a non-square rectangle and an equilateral triangle. Use folds to explain each count.
Original chapter companion covering line symmetry, grid reflections and symmetry counts for familiar shapes. It does not reproduce or solve every textbook exercise.
Original HelioLearn teaching and questions. Source-aligned companion; not an official NCERT/CBSE publication or full textbook solution bank. Independent teacher review and narrated video are pending.
