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
Notes
Euler’s formula:
For any polyhedron, F + V – E = 2
Where ‘F’ stands for a number of faces, V stands for a number of vertices and E stands for a number of edges. This relationship is called Euler’s formula.
| Solid | Shape | F | V | E | F + V | E + 2 |
| Cuboid |  |
6 | 8 | 12 | 14 | 14 |
| Triangular Pyramid |  |
4 | 4 | 6 | 8 | 8 |
| Triangular Prism |  |
5 | 6 | 9 | 11 | 11 |
| Pyramid with square base |  |
5 | 5 | 8 | 10 | 10 |
| Prism with square base |  |
6 | 8 | 12 | 14 | 14 |
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