Important Questions and Answers for Class 7 Maths Chapter 6 Constructions And Tilings 2025-26

1. Multiple choice questions.

1. Which geometric tool is NOT required for constructing the perpendicular bisector of a line segment as per the chapter?

• (a) Unmarked ruler
• (b) Set square
• (c) Compass
• (d) Rope

Answer: (b) Set square

2. What is the measure of each angle when a 360° angle is divided into 8 equal parts?

• (a) 60°
• (b) 45°
• (c) 30°
• (d) 90°

Answer: (b) 45°

3. Which of the following shapes can tile the plane completely without gaps or overlaps?

• (a) Circle
• (b) Square
• (c) Oval
• (d) Triangle with unequal sides

Answer: (b) Square

4. In the construction of a regular hexagon, how many equilateral triangles can be arranged around a point to make the hexagon?

• (a) 3
• (b) 4
• (c) 5
• (d) 6

Answer: (d) 6

2. Very Short Answer (VSA).

1. What is meant by the bisection of a line segment?

Answer: Bisection of a line segment means dividing the segment into two equal parts, often using a perpendicular bisector.

2. Which regular polygon is formed by arranging six equilateral triangles together?

Answer: Arranging six equilateral triangles together forms a regular hexagon.

3. What is tiling in mathematics?

Answer: Tiling means covering a region with shapes without leaving gaps or overlapping.

4. Name two geometric tools required to construct an angle bisector.

Answer: To construct an angle bisector, you need a ruler and a compass.

3. Short Answer Questions.

1. How do you construct a 90° angle at a specific point on a line with only a ruler and compass?

Answer: First, pick a point O on the line. Mark two points X and Y at equal distances from O using a compass. Draw arcs from X and Y above and below the line with equal radius. The intersection points define a line passing through O which is the required 90° angle.

2. What strategy does the chapter suggest to check if a rectangular grid can be tiled using 2 × 1 tiles?

Answer: The chapter suggests checking if the number of unit squares in the grid is even. If both rows and columns are even, tiling is possible by covering each column (or row) with vertical (or horizontal) tiles, ensuring every square is neatly covered.

3. Explain why any point equidistant from the ends of a line segment must lie on its perpendicular bisector.

Answer: Any point with equal distance from both endpoints of a segment satisfies the definition of a perpendicular bisector because all such points fall exactly at the middle, ensuring equal segments on both sides. This is justified using triangle congruence.

4. Why can regular hexagons tile the plane without gaps?

Answer: Regular hexagons can tile the plane because arranging six around a point sums to 360°, leaving no gaps. Each angle in a hexagon is 120°, and the edge lengths match, allowing complete coverage of space.

4. True or False Questions.

1. A perpendicular bisector of a line segment divides the segment into two equal parts at a right angle.

Answer: True

2. A regular pentagon can be easily constructed using only a ruler and compass, as described in this chapter.

Answer: False

3. In tiling, shapes can overlap as long as they cover the entire region.

Answer: False

4. It is possible to construct a 45° angle by bisecting a 90° angle.

Answer: True

3. Fill in the Blanks Questions.

1. The tool used in ancient India for geometric constructions, instead of a compass, was a ______.

Answer: rope

2. In a regular hexagon, the internal angle at each vertex is ______ degrees.

Answer: 120

3. To draw the perpendicular bisector of a segment, arcs are drawn from both endpoints with ______ radius.

Answer: equal

4. Covering a surface using repeated shapes without gaps is called ______.

Answer: tiling

Why Understanding Constructions and Tilings in Class 7 Maths Matters

Explore construction and tilings class 7 to strengthen your geometry foundations. Learning how to use ruler and compass helps you visualize shapes and solve geometrical construction class 7 questions and answers. These topics build logical thinking for later chapters and everyday life.

Practicing with class 7 maths chapter 7 worksheet with answers pdf and extra question answer sets boosts your skills. You’ll gain confidence in answering important questions class 7 maths chapter 6 constructions and tilings solutions for exams and projects. Step-by-step methods help with practical geometry and creative designs.

Understanding tiling patterns and bisection techniques connects concepts from class 7 ganita prakash chapter 7 and class 7 maths chapter 1. These real-life geometry examples inspire you for further studies like class 7 maths practical geometry extra questions and creative projects.