RBSE Solutions Class 6 Maths Chapter 11 Symmetry Exercise 11.1

Symmetry Ex 11.1

Question 1. (a) Identify the shapes given below. Check whether they are symmetric or not.
(b) Which of the above shapes have more than one lines of symmetry?
Answer:
(a) Symmetric shapes: (i) Pot, (ii) Glass, (iv) Drum, (v) Up arrow.
Non-symmetric shapes: (iii) Mug with handle, (vi) Kettle, (vii) Broom. Many everyday objects show perfect symmetry when designed.
(b) Figure (iv) (Drum) has more than one line of symmetry. A cylindrical drum has infinite lines of symmetry if viewed as a 3D object, and two if viewed as a 2D rectangle.
In simple words: Look at each picture. Some shapes can be folded exactly in half to match both sides, these are symmetric. Other shapes cannot be folded like that. Only one of the symmetric shapes has more than one way to fold it perfectly in half.

🎯 Exam Tip: When identifying symmetry in objects, consider if there's a line you can draw where both sides would be mirror images. For objects like mugs or kettles, handles break the symmetry.

Question 2. Examine the alphabets given below for the existence of symmetry.
(i) Which of the above alphabets are not symmetrical?
(ii) Which of the above alphabets are symmetrical?
(iii) Which of the above alphabets have vertical line of symmetry?
(iv) Which of the above alphabets have horizontal line of symmetry?
(v) Which of the above alphabets have vertical as well as horizontal line of symmetry?
(vi) Which of the above alphabets have more than two line of symmetry?
Answer:
Based on the given alphabet diagrams:
(i) Alphabets that are not symmetrical: G, N, Z. These letters cannot be divided into two mirror-image halves.
(ii) Alphabets that are symmetrical: A, B, C, D, E, H, K, W. These letters can be folded perfectly along at least one line.
(iii) Alphabets with a vertical line of symmetry: A, H, W. If you draw a line straight down the middle, both sides match.
(iv) Alphabets with a horizontal line of symmetry: B, C, D, E, H, K. If you draw a line straight across the middle, the top and bottom halves match.
(v) Alphabets with both vertical and horizontal lines of symmetry: O, I, H. These letters look the same when folded horizontally or vertically. Letters like O and I (though not pictured explicitly) also fall into this category.
(vi) Alphabets with more than two lines of symmetry: O. The letter O has an infinite number of lines of symmetry, as you can draw a line through its center in any direction and get a mirror image.
In simple words: Some letters can be split in half perfectly, either up-and-down or side-to-side, or both ways. Some letters cannot be split perfectly at all. The letter 'O' is special because you can split it in half in endless ways.

🎯 Exam Tip: When checking for symmetry in alphabets, imagine drawing a vertical or horizontal line through the letter. If both sides are exact mirror images, it has that type of symmetry. Some letters have both!

Question 3. Describe the number of symmetrical lines in the figure below.
Answer:
(i) Square: 4 lines of symmetry. A square can be folded along its two diagonals and two lines passing through the midpoints of opposite sides.
(ii) Isosceles triangle: 1 line of symmetry. This type of triangle has only one line that divides it into two identical halves.
(iii) Cross of arrows: 2 lines of symmetry. This shape can be folded horizontally and vertically to match perfectly.
(iv) Oval with horizontal and vertical arrows: 2 lines of symmetry. An oval shape has a horizontal and a vertical line of symmetry.
(v) Three-bladed propeller/star: 3 lines of symmetry. This shape has three lines that pass through its center, dividing it into identical sections.
In simple words: We count how many ways each picture can be cut or folded so that both halves are exactly the same. For example, a square has four ways, while a regular triangle only has one.

🎯 Exam Tip: Remember that a line of symmetry must create a mirror image on both sides. For regular polygons, the number of lines of symmetry usually matches the number of sides.

Question 4. Make different shapes having two lines of symmetry in each of them.
Answer:
Shapes that have exactly two lines of symmetry include:
1. Rectangle: It has a vertical and a horizontal line of symmetry through its center.
2. Rhombus: It has two diagonal lines of symmetry.
3. Oval/Ellipse: It has a major axis and a minor axis as lines of symmetry.
4. A plus sign (+) or cross shape: This also has two lines of symmetry (horizontal and vertical).
In simple words: We can draw many shapes that can be cut into two equal mirror halves in only two different ways. Examples are a regular window pane or a simple plus sign.

🎯 Exam Tip: Visualizing how a shape would look if folded or cut is key to finding lines of symmetry. Shapes with two lines of symmetry often have opposite sides or angles that are equal.

Question 5. List ten objects you find in your home or school and draw their figures in your notebook. Which of them are symmetric and which are not? Can you identify the lines of symmetry for those objects which are symmetric?
Answer:
Here is a list of ten objects from home or school, with their symmetry noted:
1. **Window (rectangular):** Symmetric. It has 2 lines of symmetry (one vertical and one horizontal).
2. **Bangle (circular):** Symmetric. It has infinite lines of symmetry, as any line through its center is a line of symmetry.
3. **Chapatti (circular):** Symmetric. Similar to a bangle, a chapatti has infinite lines of symmetry.
4. **Blackboard (rectangular):** Symmetric. It has 2 lines of symmetry (one vertical and one horizontal).
5. **Book (rectangular):** Symmetric. It has 2 lines of symmetry (one vertical down the middle and one horizontal across the middle).
6. **C.D. (circular):** Symmetric. A compact disc has infinite lines of symmetry, just like any other circle.
7. **Table (rectangular top):** Symmetric. Most rectangular tables have 2 lines of symmetry (one vertical and one horizontal).
8. **Mobile phone:** Symmetric. It typically has 1 line of symmetry (vertical, down the center).
9. **Spoon:** Not symmetric. Due to its curved bowl and handle, a spoon cannot be folded to make exact halves.
10. **Chair:** Not symmetric. Unless it's a very specific design, a chair usually has uneven parts (arms, back, legs) that prevent perfect symmetry. Many everyday items have symmetry to make them visually pleasing or functional.
In simple words: We looked around our homes and schools for 10 things. We checked if each thing could be cut in half perfectly, so both sides looked the same. For the ones that could, we noted how many ways they could be cut like that.

🎯 Exam Tip: When identifying objects, choose clear examples where symmetry is obvious or clearly absent. For symmetric objects, clearly state the number and orientation of the lines of symmetry.