#### Topics

##### Similarity

- Property of three parallel lines and their transversals
- Property of an Angle Bisector of a Triangle
- Basic Proportionality Theorem Or Thales Theorem
- Converse of Basic Proportionality Theorem
- Appolonius Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Similarity
- Properties of Ratios of Areas of Two Triangles
- Similarity of Triangles
- Similar Triangles
- Similarity Triangle Theorem
- Areas of Two Similar Triangles
- Areas of Similar Triangles

##### Pythagoras Theorem

##### Circle

- Theorem of External Division of Chords
- Theorem of Internal Division of Chords
- Converse of Theorem of the Angle Between Tangent and Secant
- Theorem of Angle Between Tangent and Secant
- Converse: If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
- Corollary of Cyclic Quadrilateral Theorem
- Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
- Corollaries of Inscribed Angle Theorem
- Inscribed Angle Theorem
- Intercepted Arc
- Inscribed Angle
- Property of Sum of Measures of Arcs
- Tangent Segment Theorem
- Converse of Tangent Theorem
- Circles Passing Through One, Two, Three Points
- Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
- Cyclic Properties
- Tangent - Secant Theorem
- Cyclic Quadrilateral
- Angle Subtended by the Arc to the Point on the Circle
- Angle Subtended by the Arc to the Centre
- Introduction to an Arc
- Touching Circles
- Number of Tangents from a Point on a Circle
- Tangent to a Circle
- Tangents and Its Properties
- Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Co-ordinate Geometry

##### Geometric Constructions

- To Construct Tangents to a Circle from a Point Outside the Circle.
- Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given
- Construction of Tangent Without Using Centre
- Construction of Tangents to a Circle
- Construction of Tangent to the Circle from the Point on the Circle
- Basic Geometric Constructions
- Division of a Line Segment

##### Trigonometry

##### Mensuration

#### formula

Euler’s formula ⇒ F + V – E = 2.

#### 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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