Download Geometric Twins – NCERT Class 7 Maths Chapter 9 PDF from the new NCERT Class 7 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. Two figures are congruent if they have the same shape and the same size. Tracing one and placing it on the other, it fits exactly. The figure may be rotated or flipped first.
Geometric Twins PDF – Chapter 9 of Ganita Prakash (Part II)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 9 PDF | Geometric Twins | View PDF |
| Full book | NCERT Class 7 Maths – Ganita Prakash | View Book |
Read Online
What Is in Geometric Twins? (Class 7 Maths Chapter 9)
- Two figures are congruent if they have the same shape and the same size. Tracing one and placing it on the other, it fits exactly. The figure may be rotated or flipped first.
- Arm lengths alone do not fix a figure. Two arms of 4 cm and 8 cm can be opened at any angle, so the angle between them must also be measured.
- For triangles, three sides are enough: SSS. So are two sides with the angle between them (SAS), and two angles with a side (ASA or AAS).
- Two conditions fail. AAA gives the same shape but any size, and SSA (two sides and a non-included angle) can give two different triangles.
- In a right-angled triangle, the right angle with the hypotenuse and one more side is enough — the RHS condition.
- Congruence is a tool, not just a test. It proves that angles opposite equal sides are equal, and hence that every angle of an equilateral triangle is 60°.
Quick revision – Geometric Twins
| Condition | What must be equal | Guarantees congruence? | Example from the chapter |
|---|---|---|---|
| Congruent figures | Same shape and same size | They superimpose exactly | Trace and place one on the other |
| Rotate or flip | Allowed before superimposing | Still congruent | The two teardrops on page 3 |
| Circle | Radius only | Yes | Equal radii → congruent circles |
| Rectangle | Length and breadth | Yes | All four angles are already 90° |
| SSS | Three pairs of sides | Yes | 4 cm, 6 cm, 8 cm |
| SAS | Two sides and the included angle | Yes | 6 cm, 5 cm and ∠A = 30° |
| SSA | Two sides and a non-included angle | No | 6 cm, 4 cm, 30° gives two triangles |
| AAA | All three angles | No | 30°, 70°, 80° — same shape, any size |
| ASA | Two angles and the included side | Yes | 50°, BC = 5 cm, 30° |
| AAS | Two angles and a non-included side | Yes | 35°, 75°, BC = 4 cm |
| RHS | Right angle, hypotenuse and one side | Yes | ∠B = 90°, AC = 5 cm, BC = 4 cm |
| Isosceles triangle | Angles opposite equal sides | They are equal | AB = AC → ∠B = ∠C |
| Equilateral triangle | All three angles | Each is 60° | 3 × angle = 180° |
Old NCERT vs New – Class 7 Maths
This chapter is from Ganita Prakash, the new NCERT Class 7 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
Geometric Twins – Overview
| Class | Class 7 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part II |
| Chapter | 9 of 15 – Geometric Twins |
| Book pages | Part II, 1 – 22 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 7 Maths Chapter 9 – FAQs
Where can I download Geometric Twins Class 7 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 7 Maths Chapter 9 about?
Two figures are congruent if they have the same shape and the same size. Tracing one and placing it on the other, it fits exactly. The figure may be rotated or flipped first.
Is Geometric Twins from the new NCERT Class 7 Maths book?
Yes. It is chapter 9 of ganita prakash (part ii), the new NCERT Class 7 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 7 Maths Chapter 9?
Open the NCERT Solutions link above for answers to the exercise questions.