Topics
Similarity
- Properties of Ratios of Areas of Two Triangles
- Basic Proportionality Theorem
- Property of an Angle Bisector of a Triangle
- Property of Three Parallel Lines and Their Transversals
- Similarity of Triangles (Corresponding Sides & Angles)
- Relation Between the Areas of Two Triangles
- Criteria for Similarity of Triangles
- Overview of Similarity
Pythagoras Theorem
- Pythagoras Theorem
- Pythagorean Triplet
- Property of 30°- 60°- 90° Triangle Theorem
- Property of 45°- 45°- 90° Triangle Theorem
- Similarity in Right Angled Triangles
- Theorem of Geometric Mean
- Right-angled Triangles and Pythagoras Property
- Converse of Pythagoras Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Apollonius Theorem
- Overview of Pythagoras Theorem
Circle
- Circles Passing Through One, Two, Three Points
- Tangent and Secant Properties
- Secant and Tangent
- Inscribed Angle Theorem
- Intersecting Chords and Tangents
- Corollaries of Inscribed Angle Theorem
- Angle Subtended by the Arc to the Point on the Circle
- Angle Subtended by the Arc to the Centre
- Overview of Circle
Geometric Constructions
Co-ordinate Geometry
Trigonometry
- Trigonometric Ratios in Terms of Coordinates of Point
- Angles in Standard Position
- Trigonometric Ratios
- Trigonometry Ratio of Zero Degree and Negative Angles
- Trigonometric Table
- Trigonometric Identities (Square Relations)
- Angles of Elevation and Depression
- Relation Among Trigonometric Ratios
- Trigonometric Ratios of Specific Angles
Mensuration
- Introduction
- Types of Sectors
- The Quadrant
- Key Points Summary
Introduction
Have you ever cut a pizza or a pie? The piece you hold is shaped like a slice of a circle.”. In math, this specific slice of a circle has a special name: a Sector.
Understanding sectors is important because they help us calculate areas for everything from designing round clocks to graphing data using pie charts.
Types of Sectors
Minor Sector (Smaller one):
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The smaller piece of the circle
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The central angle is less than 180°
Major Sector (Larger one):
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The larger piece of the circle
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The central angle is more than 180°
The Quadrant
When the two radii are perpendicular to each other (forming a right angle of 90°), the sector formed is called a quadrant.
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A circle has four quadrants in total.
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Each quadrant is one-fourth (¼) of the entire circle.
Key Points Summary
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Sector is a pie-slice region bounded by two radii and an arc
- Minor sector = smaller piece (angle < 180°)
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Major sector = larger piece (angle > 180°)
- A quadrant is a special sector where the two radii are perpendicular (90° angle)
