Maharashtra State Board 9th Standard Geometry Syllabus - Free PDF Download
Maharashtra State Board Syllabus 2025-26 9th Standard: The Maharashtra State Board 9th Standard Geometry Syllabus for the examination year 2025-26 has been released by the MSBSHSE, Maharashtra State Board. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2025-26 Maharashtra State Board 9th Standard Geometry Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new Maharashtra State Board syllabus to prepare for their annual exam properly.
The detailed Maharashtra State Board 9th Standard Geometry Syllabus for 2025-26 is below.
Academic year:
Maharashtra State Board 9th Standard Geometry Revised Syllabus
Maharashtra State Board 9th Standard Geometry Course Structure 2025-26 With Marking Scheme
| # | Unit/Topic | Weightage |
|---|---|---|
| 1 | Basic Concepts in Geometry | |
| 2 | Parallel Line | |
| 3 | Triangles | |
| 4 | Constructions of Triangles | |
| 5 | Quadrilaterals | |
| 6 | Circle | |
| 7 | Co-ordinate Geometry | |
| 8 | Trigonometry | |
| 9 | Surface area and volume | |
| Total | - |
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Syllabus
1 Basic Concepts in Geometry
- Fundamentals of Geometrical Concepts
- Introduction
- Fundamental Geometrical Concepts
- Concept of Points
- Definition: Point
- Fundamental Concept of a Point
- Definition: Collinear Points
- Definition: Non-Collinear Points
- Real-Life Examples
- Key Points Summary
- Concept of Lines
- Definition: Line
- Definition: Concurrent Lines
- Fundamental Properties and Representation of a Line
- Planes
- Definition: Plane
- Properties of Plane
- Key Points Summary
- Co-ordinates of Points and Distance
- Betweenness
- Line Segments
- Definition: Line Segment
- Properties and Measurement of a Line Segment
- Activity: Understanding a Line Segment
- Rays
- Introduction
- Definition: Ray
- Properties and Representation of a Ray
- Conditional Statements and Converse
- Proofs
2 Parallel Line
- Concept of Transversal Lines
- Introduction
- Angles Formed by Two Lines and Their Transversal
- When Two Parallel Lines Are Cut by a Transversal
- Example 1
- Parallel Lines
- Introduction
- Definition: Parallel Lines
- Properties of Parallel Lines
- Key Points Summary
- Test for Parallel Lines
- Interior Angles Test
- Theorem: If the interior angles formed by a transversal of two distinct lines are supplementary, then the two lines are parallel.
- Corresponding Angles Test
- Theorem: If a pair of corresponding angles formed by a transversal of two lines is congruent then the two lines are parallel.
- Interior Angles Test
- Angles and Their Measurement in Higher Mathematics
- Definition: Angle
- Properties of Angle
- Corollary of Parallel Lines
- Corollary I: If a line is perpendicular to two lines in a plane, then the two lines are parallel to each other.
- Corollary II: If two lines in a plane are parallel to a third line in the plane then those two lines are parallel to each other.
3 Triangles
- Basic Concepts of Triangles
- Definition:Triangle
- Parts of a Triangle
- Basic Properties of a Triangle
- Key Points Summary
- Remote Interior Angles of a Triangle Theorem
- Theorem: The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.
- Exterior Angle of a Triangle and Its Property
- Definition: Exterior Angle
- Properties of Exterior Angles
- Example
- Key Points Summary
- Congruence of Triangles
- Isosceles Triangles Theorem
- Theorem: If Two Sides of a Triangle Are Equal, the Angles Opposite to Them Are Also Equal.
- Converse of Isosceles Triangle Theorem
- Theorem: If Two Angles of a Triangle Are Equal, the Sides Opposite to Them Are Also Equal.
- Corollary of a Triangle
- Corollary: If three angles of a triangle are congruent then its three sides also are congruent.
- Property of 30°- 60°- 90° Triangle Theorem
- Theorem: If the acute angles of a right-angled triangle have measure 30° and 60°, then the length of the side opposite to 30° angle is half the length of the hypotenuse.
- Theorem: If the acute angles of a right-angled triangle have measure 30° and 60°, then the length of the side opposite to 60° angle is `(sqrt3)/2` × hypotenuse.
- Property of 45°- 45°- 90° Triangle Theorem
- Theorem: If measures of angles of a triangle are 45°, 45°, 90° then the length of each a side containing the right angle is `1/(sqrt2)` × hypotenuse.
- Median of a Triangle
- Definition: Median
- Properties of Medians
- The Centroid
- Key Points Summary
- Property of Median Drawn on the Hypotenuse of Right Triangle
- Theorem: In a right-angled triangle, the length of the median of the hypotenuse is half the length of the hypotenuse.
- Perpendicular Bisector Theorem
- Angle Bisector Theorem
- Properties of inequalities of sides and angles of a triangle
- Similarity of Triangles (Corresponding Sides & Angles)
- Corresponding Sides
- Corresponding Angles
4 Constructions of Triangles
- Perpendicular Bisector Theorem
- Construction of Triangles
- Introduction
- Construction 1: Three Sides Given (SSS)
- Construction 2: Two Sides and Included Angle Given (SAS)
- Construction 3: Two Angles and the Included Side Given (ASA)
- Key Points Summary
- To Construct a Triangle When Its Base, an Angle Adjacent to the Base, and the Sum of the Lengths of Remaining Sides is Given.
- To Construct a Triangle When Its Base, Angle Adjacent to the Base and Difference Between the Remaining Sides is Given.
- To Construct a Triangle, If Its Perimeter, Base and the Angles Which Include the Base Are Given.
5 Quadrilaterals
- Quadrilaterals
- Introduction
- Parts of a Quadrilateral
- Reading and Writing of a Quadrilateral
- Real-Life Examples
- Key Points Summary
- Properties of a Parallelogram
- Properties of Rhombus
- Property: Diagonals of a Rhombus Bisect Its Opposite Angles.
- Properties of a Square
- Property: Diagonals of a Square Are Congruent.
- Property: Diagonals of a Square Bisect Its Opposite Angles.
- Properties of Rectangle
- Properties of Trapezium
- Tests for Parallelogram
- Theorem: If One Pair of Opposite Sides of a Quadrilateral Are Equal and Parallel, It is a Parallelogram.
- Properties of Isosceles Trapezium
- Theorem of Midpoints of Two Sides of a Triangle
- Converse of Mid-point Theorem
6 Circle
- Basic Concept of Circle
- Introduction
- Definition: Circle
- Definition: Radius
- Definition: Diameter
- Definition: Chord
- Example
- Real-Life Applications
- Key Points Summary
- Properties of Congruent Chords
- Chord
- Incircle of a Triangle
- Introduction
- Definition: In-Circle
- Definition: Incenter
- Definition: Inradius
- Step-by-Step Construction
- Key Points Summary
- Circumcircle of a Triangle
- Introduction
- Definition: Circumcircle
- Definition: Circumcenter
- Definition: Circumradius
- Step-by-Step Construction
- Position of Circumcenter in Different Triangles
- Key Points Summary
7 Co-ordinate Geometry
- The Co-ordinates of a Point in a Plane
- Co-ordinate Geometry
- Co-ordinate Axes
- Coordinates of a Point
- Important Results
- Plotting a Point in the Plane If Its Coordinates Are Given.
- Equations of Lines Parallel to the X-axis and Y-axis
- Graphs of Linear Equations
- The Graph of a Linear Equation in the General Form
8 Trigonometry
- Terms Related to Right Angled Triangle
- Trigonometric Ratios
- Relation Among Trigonometric Ratios
- Trigonometric Ratios of Specific Angles
- Trigonometric Table
- Important Equation in Trigonometry
9 Surface area and volume
- Surface Area of a Cuboid
- Volume of a Cuboid
- Surface Area of a Cube
- Volume of Cube
- Mensuration of Cylinder
- Definition: Cylinder
- Properties of a Cylinder
- Activity 1
- Activity 2
- Mensuration of Cones
- Definition: Cone
- Types of Cones
- Properties of a Cone
- Activity
- Mensuration of a Sphere
- Surface area of a sphere
- Hemisphere
- Hollow Hemisphere
