Maharashtra State Board Syllabus For 10th Standard Board Exam Geometry: Knowing the Syllabus is very important for the students of 10th Standard Board Exam. Shaalaa has also provided a list of topics that every student needs to understand.

The Maharashtra State Board 10th Standard Board Exam Geometry syllabus for the academic year 2021-2022 is based on the Board's guidelines. Students should read the 10th Standard Board Exam Geometry Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the Maharashtra State Board 10th Standard Board Exam Geometry Syllabus pdf 2021-2022. They will also receive a complete practical syllabus for 10th Standard Board Exam Geometry in addition to this.

## Maharashtra State Board 10th Standard Board Exam Geometry Revised Syllabus

Maharashtra State Board 10th Standard Board Exam Geometry and their Unit wise marks distribution

### Maharashtra State Board 10th Standard Board Exam Geometry Course Structure 2021-2022 With Marking Scheme

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

1 | Similarity | |

2 | Pythagoras Theorem | |

3 | Circle | |

4 | Co-ordinate Geometry | |

5 | Geometric Constructions | |

6 | Trigonometry | |

7 | Mensuration | |

Total | - |

## Syllabus

- 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

- 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

- 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

- 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

- 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

- 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.