CG Board Class 9 Mathematics Chapter 12 Solutions: Transformation and Symmetry in Geometrical Shapes (ज्यामितीय आकृतियों में सममिति एवं रूपांतरण) – 2026-27

1- What particular operation is happening in each of these figures? Observe, think and decide in which transformation the figure obtained is congruent to the original figure?

Exact Hindi Translation:

Bilingual Solution / :

• Step-by-step Solution / :
• English:

1. The transformations taking place in the figures are Rigid Transformations (Translation, Reflection, Rotation) and Non-Rigid Transformation (Scaling/Resizing).
2. Under Translation (Shifting), Reflection (Overturning), and Rotation (Turning), the obtained figure retains its exact size and shape. Therefore, the figure obtained in these three transformations is congruent to the original figure.
3. Under Scaling (Scaling up or down), the size changes while the shape remains similar. Thus, the figure obtained under scaling is NOT congruent to the original figure.

• Hindi:

You have to make a border for the wall of a room. Complete the following border: A, B, C, D, E, F. Look at the pattern and answer the following questions

(i) If you only had the figure ‘A’ as above, would you be able to make this complete pattern by translating, rotating or reflecting A?

(ii) Which figures can be obtained by transforming A? Which transformation will you use for this purpose?

(iii) Which transformation will you use to get D from B?

• (i) Yes, if we only had figure A, the complete border pattern can be created by applying translation, reflection, and rotation on figure A.
• (ii) Figures B, C, D, E, F can be obtained from A. Reflection (mirror flip) gives figure B from A. Translation (horizontal shift) along with reflection gives figures C, D, E, F.
• (iii) To get figure D from figure B, we use Translation (shifting horizontally to the right).
• (i) , A , A ,
• (iii) B D *

Taking ‘l’ to be the line of reflection complete the pictures: (i), (ii), (iii), (iv), (v), (vi).

• For each picture (i) to (vi), draw the identical symmetrical half on the opposite side of line ‘l’ at the same distance, creating a complete mirror image symmetrical with respect to line ‘l’.

Taking point ‘M’ to be the point of rotation, rotate the following figures as directed

(i) Clockwise by 90°

(ii) Anticlockwise by 30°

(iii) Clockwise by 60°

• (i) Rotating clockwise by 90° turns the given shape 90° to the right keeping point M fixed.
• (ii) Rotating anticlockwise by 30° turns the given shape 30° to the left keeping point M fixed.
• (iii) Rotating clockwise by 60° turns the given shape 60° to the right keeping point M fixed.

Choose any shape of your choice. Using translation, rotation, reflection design a border of the table cover.

• Select a geometric motif (e.g., a square or flower symbol). Translate it along the edge of the table cover and reflect or rotate it alternatively to construct a continuous symmetrical table cover border.

Look carefully at each of the basic pattern (motif) given on the right. Draw the next figure for each pattern. Which transformation did you use?

• Identify the rule of pattern progression in each given motif row. Draw the next motif accordingly. The primary transformation used is Translation (sliding) and Reflection (flipping).

Draw pictures of some objects that show

(i) linear symmetry

(ii) rotational symmetry

• (i) Objects showing Linear Symmetry: Butterfly, Human face, Taj Mahal, Isosceles triangle, Maple leaf.
• (ii) Objects showing Rotational Symmetry: Ceiling fan blades, Pinwheel / Windmill, Wheel of a vehicle, Starfish, Square.
• (i) : , , , ,

Take a shape of your choice, using it as the motif, create a pattern.

• Choose a motif (such as a triangle or diamond shape). Place it repeatedly on a plane without gaps or overlaps using translation and reflection to form a tessellated pattern.

Identify English alphabet, that have

(i) two lines of symmetry

(ii) No lines of symmetry

(iii) rotational symmetry

• (i) Alphabets with TWO lines of symmetry: H, I, O, X (These letters have both a horizontal and a vertical line of symmetry).
• (ii) Alphabets with NO lines of symmetry: F, G, J, L, N, P, Q, R, S, Z.
• (iii) Alphabets with Rotational Symmetry: H, I, N, O, S, X, Z (These letters look identical to their original form after a 180° rotation, i.e., order of rotation = 2).
• (i) : H, I, O, X
• (iii) : H, I, N, O, S, X, Z