NCERT Solutions Ganita Prakash Chapter 9 & 236Section 9.2 Rotational Symmetry — Figure it Out
Book page 235 Updated on2026-09-05
Q1.
Find the angles of symmetry for the given figures about the point marked •.
Answer
The three figures of page 235 and their angles of symmetry about the marked point.
(a) The plus-shaped figure (two equal bars crossing at right angles):
Angles of symmetry = 90°, 180°, 270°, 360° (4 angles, order 4)
Each quarter turn sends an arm onto the next arm.
(b) The bracket-shaped figure (a segment with a small square at each end, both on the same side):
Angle of symmetry = 360° only (1 angle, order 1)
A half turn would carry the top square to the bottom but push it to the other side of the line, so it does not fit. This figure has no rotational symmetry — though it does have a horizontal line of symmetry.
(c) The H-shaped figure:
Angles of symmetry = 180°, 360° (2 angles, order 2)
A half turn about the middle of the cross-bar swaps the two upright lines and turns the cross-bar onto itself.
Q2.
Which of the following figures have more than one angle of symmetry?
Answer
Five of the seven figures have more than one angle of symmetry.
Figure
More than one angle?
Angles of symmetry
Circle with two perpendicular diameters
Yes
90°, 180°, 270°, 360°
Triangle pointing downwards (isosceles, not equilateral)
No
360° only
Circle divided into 3 equal sectors
Yes
120°, 240°, 360°
Pinwheel with 4 curved blades
Yes
90°, 180°, 270°, 360°
The cross “X” of two straight lines
Yes
180°, 360°
Five-pointed star
Yes
72°, 144°, 216°, 288°, 360°
Segment with two semicircles on the same side (like a “B”)
No
360° only
How to decide quickly: count how many identical parts the figure has around its centre. Four blades → 4 angles; three sectors → 3 angles; five points → 5 angles. If the parts around the centre are not alike — as in the isosceles triangle and the “B” shape — the only angle of symmetry is 360°.
Careful with the triangle: it is taller than an equilateral triangle, so its three corners are not alike. It does have one line of symmetry, but no rotational symmetry. Lines and angles must always be checked separately.
Q3.
Give the order of rotational symmetry for each figure:
Answer
The order of rotational symmetry is the number of angles of symmetry — that is, how many times the figure fits onto itself in one full turn.
Figure
Order
Angles of symmetry
Slanting segment with an arrow-flag at each end (turned opposite ways)
2
180°, 360°
Two crossing lines with an arc drawn between the upper arms
1
360° only
Six-pointed star
6
60°, 120°, 180°, 240°, 300°, 360°
The three bent arms with fists (a triskelion)
3
120°, 240°, 360°
Plus sign made of five squares
4
90°, 180°, 270°, 360°
Regular pentagon
5
72°, 144°, 216°, 288°, 360°
Smallest angle of symmetry = 360° ÷ order Order 2 → 180° • Order 3 → 120° • Order 4 → 90° • Order 5 → 72° • Order 6 → 60°
About the second figure: two crossing lines by themselves would have order 2. But the small arc is drawn only between the upper pair of arms, and a half turn would carry it to the bottom. So, counting the arc as part of the figure, only the full turn works and the order is 1.