Class 10 Maths is scoring if your theorems are clear.
Most questions directly test theorem statements, applications, or proofs.
This guide covers the most important Class 10 theorems, explained simply and exam-oriented.
6
Why Theorems Matter in Class 10
Theorems help you:
- Solve proof-based questions
- Apply logic correctly
- Score full marks in geometry
- Avoid step mistakes
Memorizing statements alone is not enough. You must know where and how to apply them.
Important Class 10 Maths Theorems (Chapter-wise)
Chapter 6: Triangles
1. Basic Proportionality Theorem (Thales Theorem)
If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
Used for:
- Proving ratios
- Similar triangles questions
2. Converse of Basic Proportionality Theorem
If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.
3. Similar Triangles Theorem (AAA / SAS / SSS)
Two triangles are similar if:
- Their corresponding angles are equal
- Their sides are proportional
Very important for proofs.
4. Pythagoras Theorem
In a right-angled triangle:
(Hypotenuse)² = (Base)² + (Perpendicular)²
5. Converse of Pythagoras Theorem
If the square of one side equals the sum of squares of the other two sides, the triangle is right-angled.
Chapter 7: Coordinate Geometry
6. Distance Formula
Distance between points (x₁, y₁) and (x₂, y₂):
√[(x₂ − x₁)² + (y₂ − y₁)²]
7. Section Formula
Used to find coordinates of a point dividing a line segment in a given ratio.
8. Area of Triangle Formula
Area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
Chapter 8: Trigonometry
4
9. Trigonometric Identity
sin²A + cos²A = 1
10. Other Important Identities
- sec²A − tan²A = 1
- cosec²A − cot²A = 1
11. Trigonometric Ratios
sin A = Perpendicular / Hypotenuse
cos A = Base / Hypotenuse
tan A = Perpendicular / Base
Chapter 9: Applications of Trigonometry
12. Angle of Elevation
Angle between horizontal and line of sight when object is above eye level.
13. Angle of Depression
Angle between horizontal and line of sight when object is below eye level.
Chapter 10: Circles
4
14. Tangent Theorem
The tangent at any point of a circle is perpendicular to the radius at the point of contact.
15. Tangents from External Point
The lengths of tangents drawn from an external point to a circle are equal.
Chapter 11: Constructions
16. Construction Theorem (Similar Triangles)
Used to construct a triangle similar to a given triangle in a given ratio.
Chapter 12: Areas Related to Circles
17. Area of Circle
πr²
18. Circumference of Circle
2πr
19. Area of Sector
(θ/360) × πr²
20. Length of Arc
(θ/360) × 2πr
Chapter 13: Surface Areas and Volumes
21. Curved Surface Area of Cylinder
2πrh
22. Total Surface Area of Cylinder
2πr(h + r)
23. Volume of Cylinder
πr²h
24. Surface Area & Volume of Cone
- CSA = πrl
- Volume = (1/3)πr²h
25. Surface Area & Volume of Sphere
- Surface Area = 4πr²
- Volume = (4/3)πr³
Chapter 14: Statistics
26. Mean Formula (Grouped Data)
Mean = Σfx / Σf
27. Mode Formula
Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Chapter 15: Probability
28. Probability Formula
Probability = Number of favorable outcomes / Total outcomes
Exam Tips for Learning Theorems
- Learn statement + diagram together
- Practice writing steps in order
- Highlight key words in proofs
- Revise formulas daily
- Solve previous year questions
Final Thoughts
Class 10 important theorems are the backbone of Maths.
If you understand them well, most questions become easy.
Revise smart. Practice regularly.
And always write steps clearly in exams.