Maharashtra State Board Syllabus For 10th Standard [इयत्ता १० वी] Geometry: Knowing the Syllabus is very important for the students of 10th Standard [इयत्ता १० वी]. Shaalaa has also provided a list of topics that every student needs to understand.

The Maharashtra State Board 10th Standard [इयत्ता १० वी] Geometry syllabus for the academic year 2023-2024 is based on the Board's guidelines. Students should read the 10th Standard [इयत्ता १० वी] 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 [इयत्ता १० वी] Geometry Syllabus pdf 2023-2024. They will also receive a complete practical syllabus for 10th Standard [इयत्ता १० वी] Geometry in addition to this.

## Maharashtra State Board 10th Standard [इयत्ता १० वी] Geometry Revised Syllabus

Maharashtra State Board 10th Standard [इयत्ता १० वी] Geometry and their Unit wise marks distribution

### Maharashtra State Board 10th Standard [इयत्ता १० वी] Geometry Course Structure 2023-2024 With Marking Scheme

# | Unit/Topic | Weightage |
---|---|---|

1 | Similarity | 10 |

2 | Pythagoras Theorem | 7 |

3 | Circle | 12 |

4 | Geometric Constructions | 7 |

5 | Co-ordinate Geometry | 7 |

6 | Trigonometry | 7 |

7 | Mensuration | 10 |

Total | - |

## Syllabus

- Similarity of Triangles
- Properties of Ratios of Areas of Two Triangles
- Ratio of areas of two triangles is equal to the ratio of the products of their bases and corresponding heights.
- Areas of triangles with equal heights are proportional to their corresponding bases.
- Areas of triangles with equal bases are proportional to their corresponding heights.

- Basic Proportionality Theorem (Thales Theorem)
**Theorem**: If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion.

- Converse of Basic Proportionality Theorem
**Theorem**: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

- Property of an Angle Bisector of a Triangle
**Theorem**: The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

- Property of Three Parallel Lines and Their Transversals
**Theorem**: The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines.

- Similar Triangles
- Criteria for Similarity of Triangles
- AAA test for similarity of triangles
- AA test for similarity of triangles
- SAS test of similarity of triangles
- SSS test for similarity of triangles

- Areas of Similar Triangles
**Theorem**: When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides.

- Pythagoras Theorem
- Pythagorean Triplet
**Formula for Pythagorean triplet**:

If a, b, c are natural numbers and a > b, then [(a2+ b2),(a2 - b2),(2ab)] is Pythagorean triplet.

- 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.

- Similarity in Right Angled Triangles
**Theorem**: In a right angled triangle, if the altitude is drawn to the hypotenuse, then the two triangles formed are similar to the original triangle and to each other.

- Theorem of Geometric Mean
In a right angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided.

- Right-angled Triangles and Pythagoras Property
- In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides.

- Converse of Pythagoras Theorem
In a triangle if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle.

- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Apollonius Theorem
In Δ ABC, if M is the midpoint of side BC, then AB

^{2}+ AC^{2}= 2AM^{2 }+ 2BM^{2}

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Circles Passing Through One, Two, Three Points
- Infinite circles pass through one point.
- Infinite circles pass through two distinct points.
- There is a unique circle passing through three non-collinear points.
- No circle can pass through 3 collinear points.

- Secant and Tangent
- Tangent to a Circle
**Tangent theorem:**A tangent at any point of a circle is perpendicular to the radius through the point of contact.

- Converse of Tangent Theorem
**Theorem**: A line perpendicular to a radius at its point on the circle is a tangent to the circle. - Tangent Segment Theorem
**Theorem**: Tangent segments drawn from an external point to a circle are congruent.

- Touching Circles
- Theorem of Touching Circles
**Theorem of touching circles:**If two circles touch each other, their point of contact lies on the line joining their centres.

- Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
- Introduction to an Arc
**Arc of a circle:**Major arc and Minor arc**Central angle****Measure of an arc**

- Congruence of Arcs
- Two arcs are congruent if their measures and radii are equal.

- Property of Sum of Measures of Arcs
**Theorem:**The chords corresponding to congruent arcs of a circle (or congruent circles) are congruent.**Theorem:**Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent.

- Inscribed Angle
- Intercepted Arc
- Inscribed Angle Theorem
- The measure of an inscribed angle is half of the measure of the arc intercepted by it.

- Corollaries of Inscribed Angle Theorem
- Angles inscribed in the same arc are congruent.
- Angle inscribed in a semicircle is a right angle.

- Cyclic Quadrilateral
- Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
**Theorem**: Opposite angles of a cyclic quadrilateral are supplementry. - Corollary of Cyclic Quadrilateral Theorem
- An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle.

- Converse: If a Pair of Opposite Angles of a Quadrilateral is Supplementary, Then the Quadrilateral is Cyclic.
- If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is cyclic.

- Converse of Cyclic Quadrilateral Theorem
**Theorem:**If two points on a given line subtend equal angles at two distinct points which lie on the same side of the line, then the four points are concyclic.

- Theorem of Angle Between Tangent and Secant
- If an angle has its vertex on the circle, its one side touches the circle and the other intersects the circle in one more point, then the measure of the angle is half the measure of its intercepted arc.

- Converse of Theorem of the Angle Between Tangent and Secant
- Theorem of Internal Division of Chords
- Suppose two chords of a circle intersect each other in the interior of the circle, then the product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the

other chord.

- Suppose two chords of a circle intersect each other in the interior of the circle, then the product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the
- Theorem of External Division of Chords
- Tangent Secant Segments Theorem
- Tangent - Secant Theorem
- Angle Subtended by the Arc to the Point on the Circle
- Angle Subtended by the Arc to the Centre
- 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

- 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

- Construction of Similar Triangle
- To construct a triangle, similar to the given triangle, bearing the given ratio with the sides of the given triangle.

(i) When vertices are distinct

(ii) When one vertex is common

- To construct a triangle, similar to the given triangle, bearing the given ratio with the sides of the given triangle.
- Construction of a Tangent to the Circle at a Point on the Circle
- Using the centre of the circle.
- Without using the centre of the circle.

- To Construct Tangents to a Circle from a Point Outside the Circle.

- 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.

- Distance Formula
- Intercepts Made by a Line
- 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

- Section Formula
- The Mid-point of a Line Segment (Mid-point Formula)
- Centroid Formula
- Slope of a Line
- Slopes of X-axis, Y-axis and lines parallel to axes.
- Slope of line – using ratio in trigonometry
- Slope of Parallel Lines

- General Equation of a Line
- Standard Forms of Equation of a Line

- Trigonometric Ratios in Terms of Coordinates of Point
- Angles in Standard Position
- Trigonometric Ratios
- Trigonometric Ratios of Complementary Angles
- Trigonometry Ratio of Zero Degree and Negative Angles
- Trigonometric Table
- Trigonometric Identities
- Heights and Distances
- Problems involving Angle of Elevation
- Problems involving Angle of Depression
- Problems involving Angle of Elevation and Depression

- Application of Trigonometry

- Conversion of Solid from One Shape to Another
- Euler's Formula
- Concept of Surface Area, Volume, and Capacity
- Surface Area and Volume of Three Dimensional Figures
- Surface Area and Volume of Different Combination of Solid Figures
- Consideration of the time volume/surface area for solid formed using two or more shapes

- Frustum of a Cone
- Sector of a Circle
- Area of a Sector of a Circle
- Length of an Arc
- Segment of a Circle
- Area of a Segment
- Circumference of a Circle
- Areas of Sector and Segment of a Circle
- Area of the Sector and Circular Segment
- Length of an Arc