Chapter 18 - Symmetry Solutions for Exercise 18.1
FAQs on RD Sharma Class 7 Solutions Chapter 18 - Symmetry (Ex 18.1) Exercise 18.1 - Free PDF
1. How should I use the Vedantu RD Sharma Solutions for Class 7 Maths Chapter 18, Exercise 18.1?
These solutions are designed to guide you through the correct problem-solving methods. First, attempt the problem from Exercise 18.1 on your own. Then, use our step-by-step solutions to verify your answer or understand the correct procedure if you get stuck. Focus on the methodology used to identify lines of symmetry for each figure, as this is key to mastering the chapter.
2. What is the correct method to find the line of symmetry for any geometric figure in this exercise?
The correct method is to find an imaginary line that divides the figure into two identical, mirror-image halves. To solve the problems in Ex 18.1, you can follow these steps:
- Visually inspect the shape for any obvious axes of reflection.
- Imagine folding the shape along a line. If the two halves perfectly overlap, that fold line is a line of symmetry.
- For polygons, check for lines passing through vertices, midpoints of sides, or diagonals.
3. How many lines of symmetry does a rhombus have, and how are they determined?
A rhombus has exactly two lines of symmetry. The correct way to determine them is by drawing its diagonals. Each diagonal of the rhombus acts as a line of symmetry, splitting the figure into two congruent (identical) isosceles triangles. A common mistake is to assume the lines bisecting the sides are also lines of symmetry, which is incorrect for a rhombus.
4. Why does an isosceles triangle have only one line of symmetry while an equilateral triangle has three?
This difference is based on the equality of their sides and angles. An isosceles triangle has only two equal sides, so the only line that creates a mirror image is the one drawn from the vertex between the equal sides to the midpoint of the opposite base. An equilateral triangle has all three sides and all three angles equal, allowing a line of symmetry to be drawn from each vertex to the midpoint of the opposite side, resulting in three lines of symmetry.
5. What is a common mistake when finding the line of symmetry for an isosceles trapezium?
A common mistake with an isosceles trapezium is to assume its diagonals are lines of symmetry, which is not true. The one and only line of symmetry in an isosceles trapezium is the line that joins the midpoints of its two parallel sides. This line divides the trapezium into two perfectly overlapping halves, but the diagonals do not.
6. How does understanding line symmetry help solve practical problems?
Understanding line symmetry is not just for geometry exercises; it has real-world applications. It is a fundamental concept in engineering, art, and design for creating balanced and aesthetically pleasing structures. For example, architects use symmetry for building facades, and designers use it for creating logos and patterns. Mastering this concept in Class 7 builds a strong foundation for more advanced topics in geometry and trigonometry.
7. Can a shape have no line of symmetry? How would I identify this in Exercise 18.1?
Yes, a shape can have zero lines of symmetry. Such a figure is called asymmetrical. A good example is a scalene triangle, where all sides and angles are different. To identify this in Exercise 18.1, you would test all possible lines (through vertices, midpoints, etc.). If no single line can divide the figure into two mirror-image halves, it has no line of symmetry.
