GRADE 4 · A4 PRINT VIEW
Fun with Symmetry · Answer guide
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Lesson 1 · Test a mirror line
Explain line symmetry using a fold or reflection.
A line of symmetry makes two halves that…
Answer: fit exactly when folded. Every point and edge must match across the fold.
For a non-square rectangle, is a diagonal a line of symmetry?
Answer: No. The diagonal makes equal-area parts, but they do not match by reflection in the diagonal.
A matching point across a mirror line is…
Answer: equally far from the line. Reflection preserves the perpendicular distance to the mirror line.
Discuss: Cut a paper rectangle with unequal adjacent sides. Test its two centre folds and one diagonal fold.
Teaching note: 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. Open responses need discussion; they are not automatically marked.
Lesson 2 · Complete a reflected pattern
Place a reflected point on the same row and at equal distance from a vertical mirror.
A point is 2 spaces left of a vertical mirror. Its image is…
Answer: 2 spaces right, same row. The image has equal distance on the opposite side and the same height.
A point lies directly on the mirror line. What happens to it?
Answer: It stays at the same position. Its distance from the mirror is zero, so it maps to itself.
A point is 4 spaces from a vertical mirror. How far apart are it and its image?
Answer: 8 spaces. There are four spaces to the line and four more to its image: 8.
Discuss: Draw a vertical line on squared paper. Place three points on the left and reflect them one at a time.
Teaching note: Reflecting is not copying a point to any nearby place. Keep equal perpendicular distance and the same row for a vertical mirror. Open responses need discussion; they are not automatically marked.
Lesson 3 · Count symmetry lines
Find all symmetry lines of familiar regular and non-regular shapes.
How many lines of symmetry does a square have?
Answer: 4. Its two centre lines and two diagonals make four.
How many lines of symmetry does a non-square rectangle have?
Answer: 2. Only the horizontal and vertical centre lines work.
How many lines of symmetry does an equilateral triangle have?
Answer: 3. Each of its three vertices gives one line to the opposite side’s midpoint.
Discuss: Draw a square, a non-square rectangle and an equilateral triangle. Use folds to explain each count.
Teaching note: A square has four symmetry lines; a non-square rectangle has only two. Do not give every rectangle the square’s diagonal symmetry. Open responses need discussion; they are not automatically marked.
Final check · Set 1
Try one set after the lessons. Use the other set after reviewing any errors.
A symmetry line requires…
exactly matching mirror halves. All points and edges must match by reflection.
Which is a symmetry line of a non-square rectangle?
A centre line parallel to a side. The two centre lines parallel to sides are its symmetry lines.
A point is 3 spaces left of a vertical mirror. Place its image…
3 spaces right, same row. Use the same distance on the opposite side.
Two reflected points are each 2 spaces from the mirror. Their separation is…
4 spaces. 2 + 2 = 4.
A square has how many symmetry lines?
4. Two centre lines and two diagonals give four.
An equilateral triangle has how many symmetry lines?
3. There is one from each vertex to the opposite side’s midpoint.
Final check · Set 2
Try one set after the lessons. Use the other set after reviewing any errors.
A line cuts a shape into equal areas. Must it be a symmetry line?
No. Equal-area parts need not fit by reflection.
A diagonal of a non-square rectangle is…
not a symmetry line. Its reflected sides do not match across a diagonal.
A point 5 spaces right of a vertical mirror reflects to…
5 spaces left, same row. The perpendicular distance stays five and the side changes.
A point on the mirror maps to…
itself. Its zero distance from the line stays zero.
A non-square rectangle has how many symmetry lines?
2. Its horizontal and vertical centre lines work; diagonals do not.
Which shape has 4 symmetry lines?
A square. The square has two centre lines and two diagonal lines.
Original chapter companion covering line symmetry, grid reflections and symmetry counts for familiar shapes. It does not reproduce or solve every textbook exercise.