---
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id: "69be80e9bd8ab661878458cd"
title: "Constructions and Tilings"
board: "CBSE"
curriculum: "CBSE"
class: "Class 7"
subject: "Mathematics"
book: "Ganita Prakash II"
chapter: "Constructions and Tilings"
chapter_slug: "constructions-and-tilings"
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---

# Constructions and Tilings

This chapter covers the concepts of geometric constructions and tiling in mathematics, focusing on techniques to construct various shapes and understanding how shapes can cover regions without gaps.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash II |
| Chapter | Constructions and Tilings |
| Pages | 136-163 |

---

## Chapter Summary

### Short Summary
This chapter introduces methods of geometric constructions, including constructing perpendicular bisectors and angles, and explores the concept of tiling geometric shapes.

### Detailed Summary
The chapter begins with geometric constructions, specifically the method to construct symmetrical shapes like 'eyes' using arcs and the concept of bisection. It elaborates on the construction of a perpendicular bisector, methods used in historical contexts like the Śulba-Sūtras, and the bisection of angles. The latter part of the chapter introduces tiling, explaining how to cover areas without gaps or overlaps using shapes such as tiles, tangrams, and the implications of grid sizes on tileability.

---

## Topic-Wise Explanation

### Geometric Constructions
This section covers techniques for constructing shapes using basic tools such as a compass and ruler. Key methods include constructing symmetrical features, perpendicular bisectors, and angles, ensuring precise geometric representation.

### Tiling
Tiling is discussed in terms of filling regions with shapes such as rectangles and polygons. The chapter examines the conditions under which certain grid sizes can be tiled using specified shapes, introducing concepts of color-based reasoning to determine tileability.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Bisection | A division of a geometrical quantity into two identical parts, fundamental for constructing shapes like perpendicular bisectors. |
| Tileability | The ability to cover a given region with specified shapes without gaps or overlaps, significant in understanding spatial arrangements. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Perpendicular Bisector | A line that divides another line segment into two equal parts at a right angle. |
| Tangram | A dissection puzzle consisting of seven flat pieces that can form various shapes when arranged correctly. |

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## Important Points for Revision

* Construction methods utilize only a compass and an unmarked ruler.
* The perpendicular bisector is crucial for creating symmetry in shapes.
* Angles can be bisected to create equal divisions, influencing various geometric constructions.
* Tiling requires understanding whether shapes can fit together without overlaps or gaps based on the grid structure.
* Color-based methods can simplify tiling problems, identifying potential solutions and limitations.

---

## Practice Questions

### Short Answer Questions
1. Explain how to construct a perpendicular bisector using a compass and ruler.
2. What properties do the angles bisected possess?
3. Describe the significance of the Śulba-Sūtras in geometric constructions.
4. How can tiling be defined in mathematical terms?
5. Give an example of a grid that can or cannot be tiled with 2 × 1 tiles.

### Long Answer Questions
1. Discuss the process and reasoning behind constructing a 90° angle using a compass and ruler.
2. Explain the implications of grid dimensions on tileability with 2 × 1 tiles, providing examples from the chapter.
3. Describe different methods of constructing the same geometric angle and evaluate their effectiveness.

---

## Related Concepts

* Congruence properties of triangles
* Angle measurement techniques
* Historical geometric methods

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69be80e9bd8ab661878458cd |
| Canonical URL | https://www.edzy.ai/cbse-class-7-mathematics-ganita-prakash-ii-constructions-and-tilings |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-7-mathematics-ganita-prakash-ii-constructions-and-tilings.md |