Quick Revision Notes: Class 6 Mathematics

Chapter: Understanding Elementary Shapes

A line segment is a fixed part of a line with two endpoints.

By Eye Estimation: Just looking at the shapes to guess length (not always accurate).
By Ruler: Placing the zero mark of the ruler at one end point and reading the mark at the other end.
By Divider: Using a divider and ruler together for more accurate measurement without errors due to thickness or eye position.

Angles are made when corners are formed. We measure them in degrees.

Right Angle (समकोण): Exactly 90° (1/4th of a revolution).
Straight Angle (सरल कोण): Exactly 180° (1/2 of a revolution).
Complete Angle (संपूर्ण कोण): Exactly 360° (1 full revolution).
Acute Angle (न्यून कोण): An angle smaller than a right angle (between 0° and 90°).
Obtuse Angle (अधिक कोण): An angle greater than a right angle but less than a straight angle (between 90° and 180°).
Reflex Angle (प्रतिवर्ती कोण): An angle greater than 180° and less than 360°.

We use a Protractor (चांदा) to measure angles.
The measure of a right angle is 90° and a straight angle is 180°.
A circle is divided into 360 equal parts, where each part is called a degree (°).

When two intersecting lines form a right angle (90°) with each other, they are called Perpendicular lines.
If line $AB$ is perpendicular to line $CD$, we write it as: $AB \perp CD$.

Triangles can be classified based on their sides and angles.

Scalene Triangle (विषमबाहु त्रिभुज): All three sides are of different lengths.
Isosceles Triangle (समद्विबाहु त्रिभुज): Exactly two sides are of equal length.
Equilateral Triangle (समबाहु त्रिभुज): All three sides are of equal length.

Acute-angled Triangle (न्यूनकोण त्रिभुज): All three angles are acute (less than 90°).
Right-angled Triangle (समकोण त्रिभुज): Exactly one angle is a right angle (90°).
Obtuse-angled Triangle (अधिककोण त्रिभुज): Exactly one angle is an obtuse angle (greater than 90°).

A polygon is a simple closed curve made up entirely of line segments.

Number of Sides (भुजाओं की संख्या)	Name of Polygon (बहुभुज का नाम)
3	Triangle (त्रिभुज)
4	Quadrilateral (चतुर्भुज)
5	Pentagon (पंचभुज)
6	Hexagon (षट्भुज)
8	Octagon (अष्टभुज)

A 4-sided polygon is a quadrilateral. Important types include:

Rectangle (आयत): Opposite sides are equal, and all four angles are right angles (90°).
Square (वर्ग): All four sides are equal, and all four angles are right angles (90°).
Parallelogram (समांतर चतुर्भुज): Opposite sides are parallel and equal.
Rhombus (समचतुर्भुज): All four sides are equal, but angles are not necessarily 90°.
Trapezium (समलंब चतुर्भुज): One pair of opposite sides is parallel.

Shapes that have length, breadth, and height (or depth) are called 3D shapes or solid shapes.

Cuboid (घनाभ): Has 6 faces, 12 edges, and 8 vertices (e.g., Matchbox, Brick).
Cube (घन): A cuboid with equal length, breadth, and height (e.g., Dice).
Cylinder (बेलन): Has 2 flat circular faces and 1 curved face (e.g., Pipe, Candle).
Cone (शंकु): Has 1 circular flat base and 1 curved surface tapering to a point (e.g., Ice-cream cone, Joker's cap).
Sphere (गोला): Has only 1 curved surface, perfectly round (e.g., Football, Globe).
Pyramid (पिरमिड): Has a polygon base and triangular faces meeting at a common top point.