NCERT Solutions for Class 7th Maths Chapter 1 Geometric Twins
Updated on 2026-09-19
About this chapter
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 equ
- Geometric Twins
- Congruence of Triangles
- Angles of Isosceles and Equilateral Triangles
Quick revision
| 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° |
Exercises
- In-text Questions — Geometric Twins Page 1–3
- Figure it Out — Geometric Twins Page 3–4
- In-text Questions — Congruence of Triangles · Measuring the Sidelengths · Conventions to Express Congruence Page 5–8
- Figure it Out — Congruence of Triangles Page 8–9
- Measuring the Angles · Two Sides and the Included Angle (SAS) · A Non-included Angle (SSA) · Two Angles and the Included Side (ASA) — In-text Questions Page 9–13
- Figure it Out — Congruence of Triangles Page 13–14
- Measuring Two Angles and a Non-Included Side (AAS) · Measuring Two Sides in a Right Triangle (RHS) — In-text Questions Page 14–17
- In-text Questions — Angles of Isosceles and Equilateral Triangles · Congruent Triangles in Real Life Page 17–20
- Figure it Out — Angles of Isosceles and Equilateral Triangles Page 20–21
- Puzzle Time