द्विविमीय आकृतियाँ
2D Shapes
A two-dimensional shape has length and breadth but no thickness. In Classes 1 to 5 a child learns to recognise, name, draw and classify plane figures by their sides, angles and symmetry — the base on which all later geometry is built.
Polygons by number of sides
| Sides | Name | Angle sum |
|---|---|---|
| 3 | Triangle | 180 degrees |
| 4 | Quadrilateral | 360 degrees |
| 5 | Pentagon | 540 degrees |
| 6 | Hexagon | 720 degrees |
| 7 | Heptagon | 900 degrees |
| 8 | Octagon | 1080 degrees |
Angle sum of a polygon = (n - 2) x 180 degrees
Triangles
- By sides — equilateral (all three equal), isosceles (two equal), scalene (all different).
- By angles — acute (all angles less than 90), right (one angle exactly 90), obtuse (one angle more than 90).
- A triangle can be both isosceles and right-angled, so the two classifications are independent.
- The sum of any two sides is always greater than the third side.
Quadrilaterals
| Shape | Defining property |
|---|---|
| Square | Four equal sides, four right angles |
| Rectangle | Opposite sides equal, four right angles |
| Rhombus | Four equal sides, opposite angles equal |
| Parallelogram | Opposite sides parallel and equal |
| Trapezium | Exactly one pair of parallel sides |
Every square is a rectangle and also a rhombus, but not every rectangle is a square. This inclusion is a favourite question and children find it genuinely difficult, because in daily talk a square is 'not a rectangle'.
Perimeter and area of plane shapes
Perimeter is the distance around a figure and is measured in units of length; area is the surface covered and is measured in square units. For a rectangle the perimeter is twice the sum of length and breadth, and the area is length times breadth. For a square the perimeter is four times a side and the area is the side squared. Children routinely confuse the two, so the units are the quickest check: centimetres for perimeter, square centimetres for area.
Circle terms
Radius joins the centre to the boundary. Diameter passes through the centre and equals twice the radius. A chord joins any two points on the circle; the diameter is the longest chord. Circumference is the boundary length, and an arc is a part of it.
✗ A square is not a rectangle because its sides are equal. | ✓ A square is a rectangle with all four sides equal.
संकेत: बहुभुज का कोण योग = (n - 2) × 180 डिग्री; वर्ग एक विशेष आयत भी है और विशेष समचतुर्भुज भी।
Geometry gives 2-3 questions in the Maths section. Most are direct property or classification items. The reliable trap is the square-rectangle inclusion, and a second is a triangle described as both isosceles and right-angled, which candidates reject as impossible. Learn the angle-sum formula because it is the fastest way to answer any polygon question. Note that CTET Paper 1 keeps the level at Class 5, so no proofs are needed — only properties and recognition.
Frequently asked questions
Is a square a rectangle?
Yes. A rectangle is a quadrilateral with four right angles and opposite sides equal, and a square satisfies both conditions with the extra property that all four sides are equal. Every square is a rectangle, but not every rectangle is a square.
What is the sum of the angles of a quadrilateral?
360 degrees. This follows from the formula for a polygon, where the angle sum equals n minus two, multiplied by 180 degrees, giving two times 180 for a four-sided figure.
What is the longest chord of a circle?
The diameter. Every chord joins two points on the circle, and the chord that passes through the centre is the longest possible one, equal to twice the radius.
60-second recap
- A 2D shape has length and breadth only; angle sum = (n - 2) x 180.
- Triangles: by sides equilateral, isosceles, scalene; by angles acute, right, obtuse.
- Every square is a rectangle and a rhombus; the reverse is not true.
- Trapezium has exactly one pair of parallel sides.
- Diameter = 2 x radius and is the longest chord.