Academic year:

## Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Similarity | - |

200 | Pythagoras Theorem | - |

300 | Circle | - |

400 | Co-ordinate Geometry | - |

500 | Geometric Constructions | - |

600 | Trigonometry | - |

700 | Mensuration | - |

Total | - |

## Syllabus

100 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
- Similar triangles
- Criteria of Similarity

- AA Criterion of similarity

- SAS Criterion of similarity

- SSS Criterion of similarity - Construction of similar triangles

- Properties of Ratios of Areas of Two Triangles
- Similarity of Triangles
- Similar Triangles
- Similarity Triangle Theorem
If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar

- Areas of Two Similar Triangles
- Areas of Similar Triangles

- Properties of ratios of areas of two triangles
- Basic proportionality theorem
- Introduction to similarity
- Similar triangles
- Areas of two similar triangles
- Similarity in right angled triangles
- Pythagoras theorem and its converse
- 30
^{o}-60^{o}-90^{o}theorem and 45^{o}-45^{o}-90^{o}theorem - Application of Pythagoras theorem in acute and obtuse angle.
- Appolonius theorem

200 Pythagoras Theorem

300 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
- Opposite Angles of a Cyclic Quadrilateral Are Supplementary
- The Exterior Angle of a Cyclic Quadrilateral is Equal to the Opposite Interior Angle (Without Proof)

- 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
- Tangent to a Circle
Theorem - The tangent at any point of a circle is perpendicular to the radius through the point of contact.

- 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
Theorem - The Length of Two Tangent Segments Drawn from a Point Outside the Circle Are Equal

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

- Tangents and its properties
- Theorem - Tangent at any point to the circle is perpendicular to the radius and its converse
- Number of tangents from a point to a circle
- Theorem- The length of two tangent segments drawn from a point outside the circle are equal
- Touching circles
- Introduction to an arc
- Angle subtended by the arc to the centre and to the point on the circle
- Cyclic quadrilateral
- Tangent - Secant theorem

400 Co-ordinate Geometry

- Centroid Formula
- The Mid-point of a Line Segment (Mid-point Formula)
- Section Formula
- Division of a Line Segment
- Division of Line Segment in a Given Ratio
- Construction of a Triangle Similar to a Given Triangle
- To divide a line segment in a given ratio
- To construct a triangle similar to a given triangle as per given scale factor

- Distance Formula
- Coordinate Geometry
- General Equation of a Line
- Standard Forms of Equation of a Line
- Intercepts Made by a Line
- Slope of a Line

- Slope of a line
- Intercepts made by a line
- Standard forms of equation of a line
- General equation of a line

500 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 Out Side the Circle
- To construct the tangents to a circle from a point outside it

- Construction of Tangent to the Circle from the Point on the Circle
- Basic Geometric Constructions
- Division of a Line Segment
- Division of Line Segment in a Given Ratio
- Construction of a Triangle Similar to a Given Triangle
- To divide a line segment in a given ratio
- To construct a triangle similar to a given triangle as per given scale factor

- Division of line segment in a given ratio
- Basic geometric constructions
- Construction of tangent to the circle from the point on the circle and out side the circle.
- Construction of tangent without using centre
- Construction of triangle If the base, angle apposite to it and either median altitude is given
- Construction of a triangle similar to a given triangle

600 Trigonometry

- Application of Trigonometry
- Heights and Distances
- Problems involving Angle of Elevation
- Problems involving Angle of Depression
- Problems involving Angle of Elevation and Depression

- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Trigonometric Ratios in Terms of Coordinates of Point
- Angles in Standard Position
- Trigonometry Ratio of Zero Degree and Negative Angles

- Angles in standard position
- Trigonometric ratios in terms of coordinates of point
- Trigonometric Identities (with proof)
- Use of basic identities and their applications
- Problems on height and distance

700 Mensuration

- Conversion of Solid from One Shape to Another
- Circumference of a Circle
- Surface Area of a Combination of Solids
- Euler's Formula
- Areas of Sector and Segment of a Circle
- Area of the Sector and Circular Segment
- Length of an Arc

- Frustum of a Cone
- Concept of Surface Area, Volume, and Capacity
- Length of an Arc
- Volume of a Combination of Solids

- Length of an arc
- Area of the sector
- Area of a Circular Segment
- Euler's formula
- Surface area and volume of cuboids Spheres, hemispheres, right circular cylinders cones, frustum of a cone
- Problems based on areas and perimeter/circumference of circle, sector and segment of a circle
- Problems on finding surface areas and volumes of combinations of any two of the following :- cuboids, spheres, hemispheres and right circular cylinders/ cones
- Problems involving converting one type of metallic solid into another.

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