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Chapter Analysis
Beginner23 pages • EnglishQuick Summary
The chapter on Symmetry introduces students to the concept of symmetry as a fundamental geometric attribute. Students learn about lines of symmetry, where a figure can be divided into two identical parts. The chapter explores both line and rotational symmetry, providing examples and practical exercises to identify symmetrical figures. Emphasis is placed on observing symmetry in natural and man-made objects, enhancing perceptual skills and geometric understanding.
Key Topics
- •Lines of Symmetry
- •Rotational Symmetry
- •Reflection
- •Symmetry in Geometry
- •Natural Symmetries
- •Reflectional Symmetry
Learning Objectives
- ✓Identify lines of symmetry in various shapes.
- ✓Differentiate between line symmetry and rotational symmetry.
- ✓Recognize symmetry in natural and human-made objects.
- ✓Apply the concept of symmetry in solving geometry problems.
- ✓Design figures that demonstrate a specific type of symmetry.
Questions in Chapter
Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?
Answer: Yes, there are 6, 4 and 1 lines of symmetry in the figures of flower, rangoli and butterfly respectively. There is no line of symmetry in the figures of pinwheel and cloud.
Page 219
Is there any other way to fold the square so that the two halves overlap? How many lines of symmetry does the square shape have?
Answer: No, there is no other way to fold the square. The square shape has 4 lines of symmetry.
Page 221
What if we reflect along the diagonal from A to C? Where do points A, B, C and D go? What if we reflect along the horizontal line of symmetry?
Answer: If we reflect along the diagonal from A to C, D occupies the position occupied by B earlier. A and C remain at the same place. If we reflect along the horizontal line of symmetry, D and C occupy the position earlier occupied by A and B respectively.
Page 222
In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded.
Answer: For figure (d), the paper was folded vertically and then horizontally or vice versa.
Page 223
How many lines of symmetry do these shapes have? A triangle with equal sides and equal angles?
Answer: The equilateral triangle has 3 lines of symmetry.
Page 226
Additional Practice Questions
Explain the term 'line of symmetry'.
easyAnswer: A line of symmetry is an imaginary line that divides a figure into two identical parts that are mirror images of each other when folded along that line.
How would you find rotational symmetry in objects?
mediumAnswer: To find rotational symmetry, identify if an object looks the same after some rotation less than a full circle. If it does, determine the angle(s) of rotation symmetry.
Why does a circle have infinite lines of symmetry?
hardAnswer: A circle has infinite lines of symmetry because any diameter through the centre creates two identical halves, allowing it to be symmetric along any possible line through its center.
Can a figure have reflection symmetry without rotational symmetry? Give an example.
mediumAnswer: Yes, a figure can have reflection symmetry without rotational symmetry. A simple example is a scalene triangle, which can have a vertical line symmetry but no rotational symmetry.
Create a geometric pattern using lines of symmetry.
easyAnswer: Draw a square. The diagonal and the mid-lines (both vertical and horizontal) will serve as lines of symmetry, creating a symmetrical design.