This page lists the class 10 maths theorems that have proof pages in the current NCERT Class 10 Mathematics textbook — nine numbered theorem pages in all — in the order the book presents them. They sit in three chapters: the divisibility and irrationality results of Chapter 1 Real Numbers, the proportionality and similarity theorems of Chapter 6 Triangles, and the tangent theorems of Chapter 10 Circles.
For each theorem you get the book’s own statement, the printed book page, and a link to the page that proves it. The list is maintained for the current academic session using the NCERT information available to us. If you are revising a whole chapter, begin at the Class 10 theorems hub, which groups these pages by chapter.
Every theorem in the NCERT Class 10 Maths book
| Theorem | What the book states | Book page | Page status |
|---|---|---|---|
| Chapter 1: Real Numbers | |||
| Theorem 1.2 — If a Prime Divides a², It Divides a | Let \(p\) be a prime number. If \(p\) divides \(a^2\), then \(p\) divides \(a\), where \(a\) is a positive integer. | 6 | Available |
| Theorem 1.3 — √2 is Irrational (and Proofs of Irrationality) | \(\sqrt{2}\) is irrational. | 6 | Available |
| Chapter 6: Triangles | |||
| Theorem 6.1 — Basic Proportionality Theorem (Thales Theorem) | If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. | 80 | Available |
| Theorem 6.2 — Converse of the Basic Proportionality Theorem | If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. | 82 | Available |
| Theorem 6.3 — AAA Similarity Criterion | If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar. | 87 | Available |
| Theorem 6.4 — SSS Similarity Criterion | If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar. | 88 | Available |
| Theorem 6.5 — SAS Similarity Criterion | If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. | 90 | Available |
| Chapter 10: Circles | |||
| Theorem 10.1 — Tangent is Perpendicular to the Radius | The tangent at any point of a circle is perpendicular to the radius through the point of contact. | 146 | Available |
| Theorem 10.2 — Tangents from an External Point are Equal | The lengths of tangents drawn from an external point to a circle are equal. | 149 | Available |
Use the table to jump straight to the theorem you are revising; the proof of each one lives on its own page.
How to use these theorem pages
The statement column carries the book’s own wording, the page column gives the printed book page, and the link in each row opens the page that proves the theorem. The proof pages show the construction, the working and the conclusion, so the table above is your entry point, not a replacement for those pages.
Revision order
The proofs appear in this order in the book: 1.2, 1.3, 6.1, 6.2, 6.3, 6.4, 6.5, 10.1, 10.2.
- Read Theorem 1.2 before Theorem 1.3, because the proof of Theorem 1.3 uses Theorem 1.2.
- Read Theorem 6.1 before Theorem 6.2, because Theorem 6.2 is the converse of Theorem 6.1.
- Treat Theorems 6.3, 6.4 and 6.5 as one set — the AAA, SSS and SAS similarity criteria.
- Read Theorem 10.1 before Theorem 10.2, in the order the book proves them.
Common mistakes to avoid
- Applying Theorem 6.2 without checking the ratio condition. The converse of the Basic Proportionality Theorem works only after the two sides are shown to be divided in the same ratio.
- Confusing AAA similarity with congruence. Equal corresponding angles prove that triangles are similar (same shape), not congruent (same shape and size).
- Forgetting that Theorem 10.1 holds only at the point of contact. The radius is perpendicular to the tangent at that point; the statement does not apply to other points of the circle.
- Using Theorem 1.2 without the condition that p is prime. The lemma is stated for a prime p; a composite divisor does not behave the same way.
- Calling Theorem 1.2 the Fundamental Theorem of Arithmetic. That result is Theorem 1.1 in this book; Theorem 1.2 is the prime-divisor lemma used in the irrationality proofs.
Sources and data verification
This listing is maintained for the 2026-27 academic session using the NCERT textbook information available to us. NCERT remains the authority for confirming the latest edition.
This page describes the NCERT Class 10 Mathematics textbook, official edition published on ncert.nic.in. Page numbers cited here are printed book pages, not PDF page numbers.
The theorem table covers the three chapters that contain numbered theorem pages in this edition: Chapter 1 Real Numbers, Chapter 6 Triangles and Chapter 10 Circles. It does not cover other classes, other subjects, or theorem pages outside this listing. The printed edition and its downloadable PDF can be checked on the official NCERT page for Class 10 Mathematics.
NCERT settles textbook editions and contents; CBSE settles the syllabus and examinations. Textbook contents and the examinable syllabus are not always identical, so check the current official syllabus before deciding what to prepare.
Questions students ask about these theorems
How many theorems are there in the Class 10 Maths NCERT book?
The directory above holds nine numbered theorem pages: two in Chapter 1, five in Chapter 6 and two in Chapter 10. Chapter 1 also states Theorem 1.1, the Fundamental Theorem of Arithmetic, just before Theorem 1.2; that statement is not among the linked theorem pages above, so the count of proof-page theorems stays at nine.
Which chapter has the most theorems in Class 10 Maths?
Chapter 6 Triangles has the most, with the five theorem pages Theorem 6.1 through Theorem 6.5.
What is the basic proportionality theorem in Class 10?
The Basic Proportionality Theorem is Theorem 6.1 on printed page 80, commonly called Thales’ theorem. It says that a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Theorem 6.2 on printed page 82 is the converse of this result.
Do I need to learn the proofs of Class 10 Maths theorems?
Plan to learn them. The textbook gives a proof for each theorem in the directory, and the exercise questions in these chapters are built on the theorems, so knowing the statement alone is usually not enough. Whether a proof appears in your particular paper is set by the current CBSE syllabus and sample papers, not by the textbook alone.
Which Class 10 Maths chapters have no theorems?
In this listing, only Chapters 1, 6 and 10 have numbered theorem pages. Chapters 2, 3, 4, 5, 7, 8 and 9 have none, so the table above is the full list of theorem pages in the directory.
Reference: NCERT Class 10 Mathematics textbook, official edition on ncert.nic.in.
Official source: download the NCERT textbook free from ncert.nic.in.