Mathematics · Class 6 · Symmetry · Term 3

Completing Symmetrical Figures

Practice your understanding of symmetry by completing a figure when given one half and the line of symmetry.

TL;DR:Challenge your students to move beyond just finding symmetry and become creators of it. These activities will help them understand the rules of reflection by drawing the missing half of fascinating figures.

• CBSE Learning Outcomes
• NCERT Class 6: Chapter 13 - Symmetry

About This Topic

This topic, 'Completing Symmetrical Figures', is a crucial step in developing spatial reasoning skills for Class 6 students, as outlined in the NCERT framework. It transitions students from passively identifying lines of symmetry in existing shapes to actively constructing the other half of a figure. This process deepens their understanding of symmetry as a reflection, a fundamental concept in geometry. The activities focus on the properties of reflection, specifically the idea that each point in the reflected image is equidistant from the line of symmetry as the corresponding point in the original figure.

Mastering this topic lays a strong foundation for more advanced geometric transformations like rotations and translations, which are explored in higher classes. It also enhances students' precision in drawing and their ability to visualise and manipulate shapes mentally. By engaging with vertical, horizontal, and diagonal lines of symmetry, students develop a more robust and flexible understanding of geometric properties, connecting mathematical rules to visual patterns they observe in the world around them, from art and architecture to nature.

Key Questions

1. Explain the process of completing a shape across a vertical line of symmetry.
2. Analyse an incomplete figure with a diagonal line of symmetry to draw its other half.
3. Justify why the completed figure is symmetrical based on the properties of reflection.

Learning Objectives

• Complete a symmetrical figure by drawing its other half across a vertical or horizontal line of symmetry.
• Construct the reflection of a given shape on a grid across a diagonal line of symmetry.
• Verify the symmetry of a completed figure by measuring the perpendicular distance of corresponding points from the line of symmetry.
• Articulate that reflection creates a mirror image where orientation is reversed.
• Apply the concept of symmetry to create their own simple symmetrical patterns.

Key Vocabulary

Symmetry	The quality of being made up of exactly similar parts facing each other or around an axis.
Line of Symmetry	An imaginary line that divides a shape into two identical halves that are mirror images of each other.
Reflection	A transformation that flips a figure over a line to create a mirror image.
Equidistant	At an equal distance from a point, line, or object.
Vertex (plural: Vertices)	A point where two or more lines or edges meet; a corner.

Watch Out for These Misconceptions

Common Misconception

Students often slide the half-figure (translation) instead of flipping it (reflection), resulting in an incorrect orientation.

What to Teach Instead

Emphasise that symmetry creates a 'mirror image'. Use the analogy of their left and right hands: they are symmetrical but cannot be placed perfectly on top of each other without flipping one over.

Common Misconception

When completing a figure, students might not maintain an equal distance from the line of symmetry for all points.

What to Teach Instead

Insist on measuring. Show them how to draw a perpendicular line from a key point to the line of symmetry and extend it the same distance on the other side. Using a ruler or counting squares on a grid makes this concrete.

Common Misconception

Diagonal lines of symmetry are particularly confusing; students often reflect the shape vertically or horizontally instead.

What to Teach Instead

Encourage students to turn their paper so the diagonal line of symmetry appears vertical or horizontal. This simple physical adjustment can make the reflection much easier to visualise and draw correctly.

Active Learning Ideas

Collaborative Problem-Solving

Mirror Magic

Students place a small, unbreakable mirror on the given line of symmetry of an incomplete figure. They observe the reflection in the mirror to see what the complete figure should look like and then draw the missing half.

15 min·Individual

Collaborative Problem-Solving

Graph Paper Challenge

Provide students with half a figure drawn on graph paper. They complete the figure by counting the number of squares from each vertex to the line of symmetry and plotting the corresponding points on the opposite side.

20 min·Pairs

Collaborative Problem-Solving

Fold and Trace

Students draw half a shape on one side of a folded paper, with the fold acting as the line of symmetry. They can then either trace the shape against a window or press hard with a pencil to create an impression on the other side, which they then trace over to complete the figure.

15 min·Individual

Real-World Connections

• Designing symmetrical patterns in art, such as in Rangoli or Kolam.
• Understanding the bilateral symmetry found in nature, like in butterflies, leaves, and faces.
• Recognising symmetry in architecture, for example, the design of the Taj Mahal or India Gate.
• Noticing symmetrical logos of famous brands and companies.
• Applying concepts of balance and stability in engineering, as seen in the design of aeroplanes and bridges.

Assessment Ideas

Exit Ticket

Give students an 'exit slip' with an incomplete figure on a dot grid. Their task is to complete it before the end of the class, providing a quick check of their understanding.

Quick Check

A worksheet containing a variety of incomplete figures with vertical, horizontal, and diagonal lines of symmetry. Students must complete them accurately, and marks can be given for precision.

Quick Check

Students use a checklist to review their own completed figure: 'Did I flip the shape? Are my corners the same distance from the line? If I folded it, would the edges match?'

Frequently Asked Questions

What is the difference between reflection and symmetry?

Symmetry is a property of a whole object. Reflection is the action or transformation that creates that symmetry. A figure is symmetrical if one half is a reflection of the other half across a line of symmetry.

Does the completed shape have to be a known shape like a square or a triangle?

Not at all! You can complete any figure, even a random, irregular shape. The only rule is that the completed half must be a perfect mirror image of the given half.

Why is it harder to draw with a diagonal line of symmetry?

Our brains are more used to thinking in terms of up-down (vertical) and left-right (horizontal). Diagonal lines require us to measure at an angle, which is less intuitive. Using graph paper to guide your points helps a lot.