Maharashtra State Board Syllabus For 9th Standard Geometry: Knowing the Syllabus is very important for the students of 9th Standard. Shaalaa has also provided a list of topics that every student needs to understand.

The Maharashtra State Board 9th Standard Geometry syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the 9th Standard 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 9th Standard Geometry Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for 9th Standard Geometry in addition to this.

## 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 2022-2023 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

- Introduction to Basic Concepts in Geometry
- Concept of Points
- Concept of Line
- Line
- Collinear points
- Non-collinear points
- Distance of a point from a line

- Concept of Plane
- Co-ordinates of Points and Distance
- Betweenness
- Concept of Line Segment
- Line segment
- Congruent line segments
- Properties of congruent line segments
- The midpoint of a line segment
- Comparison of line segments
- Perpendicularity of line segments

- Concept of Ray
- Ray
- Perpendicularity of rays

- Conditional Statements and Converse
- Proofs

- Parallel Lines
- Checking Parallel Lines
- Pairs of Lines - Transversal of Parallel Lines
- Properties of Parallel Lines
- Interior Angle Theorem
**Theorem:**If a Transversal Intersects Two Parallel Lines, Then Each Pair of Interior Angles on the Same Side of the Transversal is Supplementary.

- Corresponding Angle Theorem
**Theorem:**If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

- Alternate Angles Theorems
**Theorem:**If a Transversal Intersects Two Parallel Lines, Then Each Pair of Alternate Interior Angles Are Equal.

- Interior Angle Theorem
- 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.

- Alternate Angles Test
**Theorem:**If a pair of alternate angles formed by a transversal of two lines is congruent 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
- 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.

- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- 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
- An exterior angle of a triangle is equal to the sum of its interior opposite angles.
- an exterior angle of a triangle is greater than its remote interior angle.
- The sum of exterior angles of a triangle is 360°.

- 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

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Types of Quadrilaterals
- Properties of a Parallelogram
- Tests for Parallelogram
- Properties of Rectangle
- Properties of a Square
- Properties of Rhombus
- Theorem of Midpoints of Two Sides of a Triangle
- Converse of Mid-point Theorem

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Properties of Chord
- Relation Between Congruent Chords of a Circle and Their Distances from the Centre
- Properties of Congruent Chords
- Incircle of a Triangle
- Construction of the Incircle of a Triangle.
- Circumcentre of a Triangle
- Construction of the Circumcircle of a Triangle

- 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

- Surface Area of a Cuboid
- Volume of a Cuboid
- Surface Area of a Cube
- Volume of Cube
- Surface Area of Cylinder
- Right Circular Cylinder
- Hollow Cylinder

- Volume of a Cylinder
- Concept of Cone
- Cone
- Types of cone
- Properties of Right circular cone
- Terms related to a cone and their relation

- Surface Area of a Right Circular Cone
- Volume of a Right Circular Cone
- Surface Area of a Sphere
- Surface area of a sphere
- Hemisphere
- Hollow Hemisphere

- Volume of a Sphere