NCERT Class 7 Mathematics Ganita Prakash-II: Chapter 6 — Constructions and Tilings
This chapter, 'Geometric Constructions,' from NCERT Class 7 Mathematics Ganita Prakash-II, introduces the concept of constructing geometric figures with precision. It revisits the 'Eyes' construction from Grade 6, emphasizing symmetry and the use of spatial estimation. The chapter explains how to systematically find centers for drawing arcs to create symmetrical shapes. Key concepts like bisection and perpendicular bisectors are defined and illustrated. Students learn that joining points where arcs meet above and below a line segment results in the perpendicular bisector. The chapter uses congruence to prove that the line joining these points is indeed the perpendicular bisector, reinforcing fundamental geometric principles essential for CBSE learning.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash-II |
| Chapter | Chapter 6 — Constructions and Tilings |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 493 |
Learning outcomes
- Understand the concept of geometric constructions for symmetrical figures.
- Learn to systematically construct geometric shapes using arcs and centers.
- Define and identify the perpendicular bisector of a line segment.
- Apply the concept of congruence to prove geometric properties.
- Develop spatial reasoning and precision in drawing.
Vocabulary
| Word | Meaning |
|---|---|
| Symmetrical | Having corresponding parts that are balanced and proportionate. |
| Spatial estimation | The ability to estimate distances, sizes, and positions in space. |
| Bisection | The division of something into two equal or congruent parts. |
| Perpendicular bisector | A line that divides a line segment into two equal parts and is at a 90-degree angle to it. |
| Congruence | The state of being congruent; identical in form; coinciding exactly. |
| Corresponding parts | Parts of congruent figures that are in the same relative position. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- What is the purpose of constructing geometric figures symmetrically? Answer: To ensure that the figure has balanced and proportionate parts, making it visually appealing and accurate.
- Define the term 'perpendicular bisector'. Answer: A perpendicular bisector is a line that intersects a line segment at its midpoint and is perpendicular to it (forms a 90-degree angle).
- Which geometric principle is used to prove that a line is a perpendicular bisector? Answer: Congruence of triangles is used to prove that a line is a perpendicular bisector.
- If AX = AY = BX = BY for points A and B and line segment XY, what can be said about the line AB in relation to XY? Answer: The line AB is the perpendicular bisector of XY.
Frequently asked questions
What is geometric construction?
Geometric construction is the process of drawing geometric figures using only a compass and straightedge, ensuring precision and accuracy.
Why is symmetry important in geometric constructions?
Symmetry ensures that a figure is balanced and has identical halves, which is crucial for accurate and aesthetically pleasing constructions like the 'Eyes' example.
How do you find the perpendicular bisector of a line segment?
You find the perpendicular bisector by drawing arcs of the same radius from both endpoints of the line segment, above and below it. The line joining the intersection points of these arcs is the perpendicular bisector.
What does it mean for two triangles to be congruent?
Two triangles are congruent if their corresponding sides and corresponding angles are equal, meaning they are identical in shape and size.
How does congruence help in proving the perpendicular bisector?
By proving that two triangles formed by the line segment and the intersecting line are congruent, we can show that the line bisects the segment and is perpendicular to it.
Related resources
Important topics
Topics covered
NCERT Class 7 Mathematics — Ganita Prakash-II — Chapter 6 — Constructions and Tilings. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.