Quick Revision Notes: Class 6 Mathematics

Chapter: Understanding Elementary Shapes

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1. Measuring Line Segments (रेखाखंडों को मापना)

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.

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2. Angles - "Acute, Obtuse, Right and Straight" (कोण - न्यून, अधिक, सम और सरल कोण)

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°.

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3. Measuring Angles (कोणों का मापन)

• 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 (°).

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4. Perpendicular Lines (लंब रेखाएँ)

• 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: $AB \perp CD$.

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5. Classification of Triangles (त्रिभुज का वर्गीकरण)

Triangles can be classified based on their sides and angles.

Based on Sides (भुजाओं के आधार पर):

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

Based on Angles (कोणों के आधार पर):

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

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6. Polygons (बहुभुज)

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)

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7. Quadrilaterals (चतुर्भुज)

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.

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8. Three-Dimensional Shapes (त्रिविमीय आकृतियाँ)

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.