Chapter focus: Symmetry describes a balanced correspondence between parts of a figure. Students explore mirror symmetry, lines of symmetry and symmetry in familiar shapes and patterns.

🎯 Learning Goals

• Understand symmetry through reflection and matching parts.
• Identify lines of symmetry in common figures.
• Complete simple symmetric figures.
• Use folding and mirror ideas to test symmetry.
• Recognise symmetry in patterns and everyday objects.
• Explain why a figure is or is not symmetric.

🪞 1. What Is Symmetry?

A figure has symmetry when one part corresponds to another part in a balanced way. In mirror symmetry, a line acts like a mirror: corresponding points lie at equal distances on opposite sides.

📏 2. Line of Symmetry

A line of symmetry divides a figure into two matching halves. If the figure is folded along that line, the two halves can coincide.

🔷 3. Symmetry in Common Shapes

These counts depend on the exact geometric shape. A distorted drawing may not have the same symmetry as the intended mathematical figure.

🧩 4. Completing Symmetric Figures

1. Identify the proposed line of symmetry.
2. Observe the distance of each marked point from the line.
3. Place the matching point at the same perpendicular distance on the other side.
4. Join corresponding points carefully.
5. Check whether the completed figure matches under reflection.

🔍 5. Symmetry in Patterns

Symmetry appears in rangoli designs, tiles, leaves, logos, buildings, artwork and many natural forms. Look for repeated shapes and matching positions rather than judging only by appearance.

📋 Worked Examples

Example 1 – Rectangle

A non-square rectangle has 2 lines of symmetry: one through the middle horizontally and one through the middle vertically.

Example 2 – Square

A square has 4 lines of symmetry: two through opposite side midpoints and two diagonals.

Example 3 – Isosceles Triangle

An isosceles triangle has 1 line of symmetry, passing from the vertex between the equal sides to the midpoint of the opposite side.

🧠 Symmetry Reasoning

1. Why does a scalene triangle have no line of symmetry?
2. Why does a circle have infinitely many lines of symmetry?
3. Can a figure have rotational symmetry but no line of symmetry? Discuss with an example.
4. How can folding paper help test symmetry?
5. Why must corresponding points be equally distant from a line of symmetry?

📝 Important Practice Questions

1. Define symmetry.
2. What is a line of symmetry?
3. How many lines of symmetry does a square have?
4. How many does a rectangle have?
5. How many does an equilateral triangle have?
6. How many lines of symmetry does a scalene triangle have?
7. Draw a shape with exactly one line of symmetry.
8. Draw a shape with no line of symmetry.
9. Complete a half-drawn symmetric figure.
10. List three examples of symmetry from daily life.

🔥 Competency / HOTS Questions

1. A student says every rectangle has four lines of symmetry. Is this correct? Explain the difference between a rectangle and a square.
2. Can a figure have more than one line of symmetry? Give examples.
3. Design a figure with exactly two lines of symmetry.
4. Why is a slightly tilted drawing of a symmetric shape sometimes misleading?
5. Find symmetry in a traditional Indian pattern and describe its line or lines of symmetry.

🧩 MCQ Practice

1. A line that divides a figure into matching mirror halves is called — A. radius B. line of symmetry C. diameter D. scale
2. A square has — A. 1 B. 2 C. 3 D. 4 lines of symmetry.
3. A non-square rectangle has — A. 0 B. 1 C. 2 D. 4 lines of symmetry.
4. An equilateral triangle has — A. 1 B. 2 C. 3 D. 4 lines of symmetry.
5. A scalene triangle has — A. 0 B. 1 C. 2 D. 3 lines of symmetry.
6. A circle has — A. 1 B. 2 C. 4 D. infinitely many lines of symmetry.
7. Which method can help test mirror symmetry? A. folding B. weighing C. measuring temperature D. counting only vertices
8. In reflection symmetry, corresponding points are — A. random B. equally distant from the symmetry line C. always on the line D. at different scales

Answer Key: 1-B, 2-D, 3-C, 4-C, 5-A, 6-D, 7-A, 8-B

📄 Printable Worksheet

1. Draw all lines of symmetry of a square.
2. Draw the lines of symmetry of a rectangle.
3. Draw an equilateral triangle and mark its symmetry lines.
4. Draw a shape with one line of symmetry.
5. Draw a shape with two lines of symmetry.
6. Complete a half-drawn symmetric pattern.
7. Identify whether five given figures are symmetric.
8. List five symmetrical objects from your surroundings.
9. Explain the folding test for symmetry.
10. Create a symmetric rangoli-style pattern.

🔁 Quick Revision Table

✅ Chapter Mastery Checklist

• ☐ I can explain symmetry.
• ☐ I can identify lines of symmetry.
• ☐ I can count symmetry lines in common shapes.
• ☐ I can complete a symmetric figure.
• ☐ I can test symmetry by folding.
• ☐ I can identify symmetry in patterns and surroundings.

🔗 Continue Learning

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