Geometry SSC (English Medium) 9th Standard Maharashtra State Board Syllabus 2024-25

Maharashtra State Board 9th Standard Geometry Syllabus - Free PDF Download

Maharashtra State Board Syllabus 2024-25 9th Standard: The Maharashtra State Board 9th Standard Geometry Syllabus for the examination year 2024-25 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 2024-25 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 2024-25 is below.

Academic year:

Maharashtra State Board 9th Standard Geometry Revised Syllabus

Maharashtra State Board 9th Standard Geometry and their Unit wise marks distribution

Maharashtra State Board 9th Standard Geometry Course Structure 2024-25 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	-

Syllabus

1 Basic Concepts in Geometry

Introduction to Basic Concepts in Geometry
Concept of Points
- Definition
- Fundamental Concept of a Point
Concept of Line
- Introduction
- Fundamental Properties and Representation of a Line
Concept of Plane
- Definition
- Properties of Plane
Co-ordinates of Points and Distance
Betweenness
Concept of Line Segment
- Definition
- Properties and Measurement of a Line Segment
Concept of Ray
- Definition
- Properties and Representation of a Ray
Conditional Statements and Converse
Proofs

2 Parallel Line

Introduction to Parallel Lines
- Definition
- Properties of Parallel Lines
Pairs of Lines - Transversal of Parallel Lines
Properties of Parallel Lines
- Interior Angle Theorem
- Corresponding Angle Theorem
- Alternate Angles Theorems
Use of properties of parallel lines
- Theorem: The sum of measures of all angles of a triangle is 180°.
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.
Concept of Angle
- Definition
- 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

Concept of Triangles
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
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
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
Similar Triangles
Similarity of Triangles

4 Constructions of Triangles

Perpendicular Bisector Theorem
Construction of Triangles
- 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

Concept of Quadrilaterals
- Introduction:
- Reading and Writing of a Quadrilateral
Types of Quadrilaterals
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of a Square
- Properties of Rectangle
- Properties of Trapezium
- Properties of Isosceles Trapezium
Properties of a Parallelogram
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The adjacent angles in a parallelogram are supplementary.
Tests for Parallelogram
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
- Theorem: If One Pair of Opposite Sides of a Quadrilateral Are Equal and Parallel, It is a Parallelogram.
Properties of Rectangle
- Property: The Diagonals of a Rectangle Are of Equal Length.
Properties of a Square
- Property: Diagonals of a Square Are Congruent.
- Property: The diagonals of a square are perpendicular bisectors of each other.
- Property: Diagonals of a Square Bisect Its Opposite Angles.
Properties of Rhombus
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: Diagonals of a Rhombus Bisect Its Opposite Angles.
Theorem of Midpoints of Two Sides of a Triangle
Converse of Mid-point Theorem

6 Circle

Concept of Circle
Properties of Chord
- Theorem: a Perpendicular Drawn from the Centre of a Circle on Its Chord Bisects the Chord.
- Theorem : The Segment Joining the Centre of a Circle and the Midpoint of Its Chord is Perpendicular to the Chord.
Relation Between Congruent Chords of a Circle and Their Distances from the Centre
Properties of Congruent Chords
- Theorem: Equal chords of a circle are equidistant from the centre.
- Theorem : The Chords of a Circle Which Are Equidistant from the Centre Are Equal.
Incircle of a Triangle
Construction of the Incircle of a Triangle.
Circumcentre of a Triangle
Construction of the Circumcircle of a Triangle

7 Co-ordinate Geometry

Coordinate Geometry
- To find distance between any two points on an axis.
- To find the distance between two points if the segment joining these points is parallel to any axis in the XY plane.
The Co-ordinates of a Point in a Plane
Co-ordinates of Points on the Axes
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