Topics
Number Systems
Number Systems
Algebra
Polynomials
Algebraic Expressions
Algebraic Identities
Linear Equations in Two Variables
Coordinate Geometry
Coordinate Geometry
Geometry
Area
Constructions
- Introduction of Constructions
- Geometric Constructions
- Some Constructions of Triangles
Mensuration
Introduction to Euclid’S Geometry
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Concept of Pairs of Angles
- Concept of Transversal Lines
- Basic Properties of a Triangle
Probability
Triangles
Quadrilaterals
- Properties of Quadrilateral
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
CBSE: Class 10
Key Points: Graphical Method
| Condition | Nature of Lines | Number of Solutions | Type of Pair |
|---|---|---|---|
| \[\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\] | Intersecting | One (unique) solution | Consistent |
| \[\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\] | Parallel | No solution | Inconsistent |
| \[\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\] | Coincident | Infinitely many solutions | Dependent (consistent) |
