SUMMARY: The chapter on Symmetry in Class 7 Mathematics explores the concept of symmetry and its applications in geometry and real life. KEY TOPICS: Line of symmetry, reflective symmetry, rotational symmetry, symmetrical figures, mirror line, axis of symmetry, order of rotational symmetry, patterns, symmetry in nature, symmetry in art and architecture.
How many lines of symmetry does a regular hexagon have?
A3
B6
C4
D2
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Correct answer: Option 2 — 6
Q31 Mark
If a figure has rotational symmetry, what does that imply?
AIt can be folded into equal halves.
BIt looks the same after a certain rotation.
CIt has no lines of symmetry.
DIt can be divided into four equal parts.
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Correct answer: Option 2 — It looks the same after a certain rotation.
Q41 Mark
Which of the following shapes does NOT have any lines of symmetry?
ASquare
BEquilateral triangle
CKite
DScalene triangle
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Correct answer: Option 4 — Scalene triangle
Q51 Mark
A butterfly exhibits which type of symmetry?
ARotational symmetry
BLine symmetry
CTranslational symmetry
DNo symmetry
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Correct answer: Option 2 — Line symmetry
Short Answer Questions5 questions
Q63 Marks
What is symmetry in geometry?
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Symmetry in geometry refers to a balanced and proportionate similarity in shape and size on either side of a dividing line or around a central point. An object is said to be symmetrical if it can be divided into two identical halves.
Q73 Marks
How can you identify a line of symmetry in a figure?
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To identify a line of symmetry in a figure, you can fold the figure along the line. If both halves match perfectly, then the line is a line of symmetry. For example, a square has four lines of symmetry.
Q83 Marks
Give an example of a shape that has rotational symmetry and explain it.
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An example of a shape with rotational symmetry is a circle. A circle can be rotated about its center at any angle, and it will look the same at all positions. This means it has infinite lines of symmetry.
Q93 Marks
What is the difference between line symmetry and rotational symmetry?
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Line symmetry, also known as reflection symmetry, occurs when a figure can be divided into two identical halves by a line. Rotational symmetry, on the other hand, occurs when a figure can be rotated around a central point and still look the same at certain angles.
Q103 Marks
Can a figure have more than one line of symmetry? Provide an example.
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Yes, a figure can have more than one line of symmetry. For example, a rectangle has two lines of symmetry: one vertical and one horizontal. A regular hexagon has six lines of symmetry, each passing through a vertex and the midpoint of the opposite side.
Long Answer Questions5 questions
Q116 Marks
Define symmetry and explain its significance in everyday life. Provide examples of symmetrical objects found in nature and architecture.
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Symmetry is a property where one half of an object is a mirror image of the other half. It plays a significant role in aesthetics, balance, and design in various fields, including art, architecture, and nature. For instance, a butterfly exhibits bilateral symmetry, where both wings are identical in shape and size. Similarly, many buildings, such as the Taj Mahal, are designed with symmetrical features to create visual harmony and balance.
Q126 Marks
Describe the different types of symmetry: line symmetry, rotational symmetry, and point symmetry. Provide examples for each type.
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Line symmetry, also known as mirror symmetry, occurs when an object can be divided into two identical halves along a line. For example, a heart shape has line symmetry along its vertical axis. Rotational symmetry exists when an object can be rotated around a central point and still look the same at certain angles; a starfish exhibits this type of symmetry. Point symmetry means that every part of the object has a matching part at an equal distance from a central point; an example is a circle, where any point on the circumference has a corresponding point directly opposite it.
Q136 Marks
How can you determine if a shape has line symmetry? Describe the steps involved in finding the line of symmetry for a given shape.
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To determine if a shape has line symmetry, one can follow these steps: First, visually inspect the shape to identify potential lines of symmetry. Next, fold the shape along the suspected line; if both halves match perfectly, the line is indeed a line of symmetry. Alternatively, one can use a ruler to draw the line and check if the distances from the line to corresponding points on both sides are equal. For example, in a rectangle, the vertical and horizontal lines through the center serve as lines of symmetry.
Q146 Marks
Explain the concept of rotational symmetry and how to find the order of rotational symmetry of a shape. Illustrate your answer with an example.
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Rotational symmetry refers to the property of a shape that looks the same after a certain amount of rotation. The order of rotational symmetry is the number of times a shape fits onto itself during a full rotation of 360 degrees. For instance, a square has an order of rotational symmetry of 4, as it can be rotated at 90-degree intervals (0°, 90°, 180°, and 270°) and still appear unchanged. To find the order, one can rotate the shape and count the positions where it coincides with its original outline.
Q156 Marks
Discuss the importance of symmetry in art and design. How do artists and architects use symmetry to enhance their work?
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Symmetry is crucial in art and design as it creates balance, harmony, and aesthetic appeal. Artists often use symmetry to draw attention to a focal point or to create a sense of order in their work. For example, in classical architecture, symmetrical designs are employed to evoke a sense of grandeur and stability, as seen in structures like the Parthenon. In modern art, symmetry can be manipulated to create dynamic compositions that challenge traditional perceptions. Overall, symmetry helps convey emotions and messages effectively through visual means.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): A figure is symmetrical if it can be divided into two identical halves.
Reason (R): Symmetry can be observed in nature, such as in the wings of a butterfly.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): All quadrilaterals have at least one line of symmetry.
Reason (R): A square has four lines of symmetry, while a rectangle has two.
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Correct answer: Option 3 —
A is true, but R is false.
Q181 Mark
Assertion (A): A circle has an infinite number of lines of symmetry.
Reason (R): Lines of symmetry can only be drawn through the center of the circle.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q191 Mark
Assertion (A): An isosceles triangle has exactly one line of symmetry.
Reason (R): An isosceles triangle can be divided into two equal parts by its altitude from the vertex.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q201 Mark
Assertion (A): A rectangle has more lines of symmetry than a square.
Reason (R): A square has four lines of symmetry, while a rectangle has only two.
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Correct answer: Option 4 —
A is false, but R is true.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: A line of symmetry divides a shape into two identical halves.
Statement 2: All shapes have at least one line of symmetry.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q221 Mark
Statement 1: A circle has infinite lines of symmetry.
Statement 2: A rectangle has only two lines of symmetry.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q231 Mark
Statement 1: An equilateral triangle has three lines of symmetry.
Statement 2: A square has four lines of symmetry.
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Correct answer: Option 1 —
Both statements are true.
Q241 Mark
Statement 1: A regular pentagon has five lines of symmetry.
Statement 2: A trapezium has no lines of symmetry.
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Correct answer: Option 4 —
Both statements are false.
Q251 Mark
Statement 1: The letter 'A' has vertical symmetry.
Statement 2: The letter 'B' has horizontal symmetry.
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Correct answer: Option 2 —
Only Statement 1 is true.
