Are these practice questions for Constructions and Tilings based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 7 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Constructions and Tilings free?

Yes. Every chapter includes free practice questions for Class 7 students to get you started.

What types of questions are included?

The practice set for Constructions and Tilings mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Constructions and Tilings for full coverage.

How many practice questions are there for Constructions and Tilings?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Constructions and Tilings Class 7 Mathematics Practice Questions with Answers

easy

Justify why the standard compass and ruler construction for a

60^\circ

angle is geometrically correct.

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easy

Explain the key property of points lying on a perpendicular bisector which is used for its construction.

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easy

Analyze whether a standard

7 \times 7

grid can be tiled perfectly by

2 \times 1

dominoes. Justify your answer by calculating the area.

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easy

Identify the angle that is constructed when you create an equilateral triangle.

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easy

To construct an angle of

22.5^\circ

using only a ruler and compass, which two geometric constructions must be applied in sequence? Analyze the steps.

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easy

Demonstrate the construction of a regular hexagon with a side length of 4 cm. After constructing the hexagon, construct its circumcircle (the circle passing through all its vertices).

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easy

What is meant by 'tiling' in geometry?

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easy

Define the term 'perpendicular bisector'.

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easy

Name the two fundamental tools that are used for basic geometric constructions.

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easy

Describe the meaning of 'bisection' in geometry and provide one example for a line segment and one for an angle.

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medium

Demonstrate how to find a point P on a given line segment AB of length 8 cm such that AP =

\frac{1}{4}

AB, using only a ruler and compass. List the steps.

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medium

The text describes a method to construct a line parallel to a given line by copying an angle. Justify why this construction is guaranteed to produce a parallel line by referencing the properties of parallel lines and transversals.

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medium

Demonstrate the steps to construct an angle of

135^\circ

using only a ruler and compass. Label the final angle.

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medium

A student claims they can construct a perpendicular bisector of a line segment XY by drawing arcs of radius 5 cm from X and arcs of radius 6 cm from Y, both above and below the line. Critique this method. Is it valid? Justify your answer.

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medium

Design and justify a method to divide a given line segment AB into four equal parts using only a ruler and compass.

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medium

Design a geometric pattern for a circular region. Describe the steps to create your design using only a ruler and compass, starting with a given circle.

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medium

Two circles with centers P and Q intersect at points A and B. The radius of both circles is 6 cm. Analyze the geometric relationship between the line segment PQ (joining the centers) and the common chord AB. Justify your analysis.

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medium

Demonstrate the construction of a design consisting of a square of side 6 cm with four semi-circles drawn on each side as a diameter, where the semi-circles point outwards from the square. Show all construction lines.

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medium

Demonstrate the construction of a triangle ABC where base AB = 7 cm,

\angle CAB = 45^\circ

, and

\angle CBA = 60^\circ

. Use only a ruler and compass and show all construction arcs.

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medium

Explain the step-by-step procedure to construct the perpendicular bisector of a line segment XY. Also, state the geometric reason why this method is accurate.

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medium

Propose a method to construct a

135^\circ

angle using only a ruler and compass. You do not need to perform the construction, only outline the steps.

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medium

Summarize the information given in the text about the Śulba-Sūtras. What were these texts, what was their main purpose, and what primary tool was used for the constructions described in them?

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medium

Summarize the method for bisecting a given angle,

\angle PQR

, using a compass and a ruler.

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medium

Create a set of instructions to construct a rhombus with diagonals of length 8 cm and 6 cm using only a ruler and compass. Justify why your construction results in a rhombus.

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medium

To construct the perpendicular bisector of a line segment PQ of length 10 cm, what is the minimum radius you must set on your compass? Analyze and explain why.

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medium

Create a step-by-step guide to construct a regular hexagon inscribed in a circle of a given radius 'r'. Justify why the side length of the resulting hexagon is precisely equal to the radius of the circle.

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medium

Describe the first two steps required to construct a

90^\circ

angle at a given point 'O' on a straight line.

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medium

List two examples of regular polygons that can be used to tile the entire plane without any gaps.

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medium

Explain the relationship between a regular hexagon and equilateral triangles that helps in the construction of the hexagon.

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medium

What is the main principle involving angles that allows for the construction of a line parallel to another given line?

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medium

When constructing a line parallel to a given line through an external point, the method involves copying an angle. Analyze which pair of angles (e.g., corresponding, alternate interior) are constructed to be equal.

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medium

Formulate a condition that must be met for an

m \times n

rectangular grid to be tileable by

1 \times 3

tiles (trominoes).

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medium

Draw a line m and a point K not on it. First, construct a line n through K parallel to m. Second, construct a line p that is perpendicular to m and passes through K. Analyze the relationship between lines n and p.

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medium

Formulate and justify a method to construct a

75^\circ

angle using only a ruler and compass.

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hard

Given an acute angle

\angle PQR

. Demonstrate the steps to construct a new angle

\angle XYZ

such that

\angle XYZ = 2 \times \angle PQR

using only a ruler and compass.

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hard

A regular hexagon can be divided into six congruent triangles by joining its opposite vertices. Analyze and identify the specific type of these triangles.

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hard

An L-shaped tromino is a tile made of three

1 \times 1

squares. Analyze if a full

8 \times 8

grid can be tiled by L-shaped trominoes. Then, analyze if an

8 \times 8

grid with any single

1 \times 1

square removed can be tiled by L-shaped trominoes. Justify your reasoning.

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hard

A student attempts to bisect

\angle ABC

. First, they draw an arc from B, cutting AB at P and BC at Q. Then, they set their compass to the length PQ and draw intersecting arcs from P and Q to find a point R. They claim the line BR bisects the angle. Critique this method. Is it always correct?

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hard

Explain the chessboard coloring argument that can be used to show that a grid with an odd number of squares cannot be tiled by

2 \times 1

dominoes.

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hard

A standard

8 \times 8

chessboard has two squares removed from opposite corners. Is it possible to tile the remaining 62 squares with

2 \times 1

dominoes? Evaluate the problem and provide a justification for your conclusion.

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hard

A

6 \times 6

chessboard has two opposite corner squares removed (e.g., top-left and bottom-right). Analyze if the remaining 34 squares can be tiled by

2 \times 1

dominoes using the coloring method.

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hard

The ancient Śulba-Sūtras used a rope to construct a perpendicular bisector. A rope of fixed length is looped onto pegs at points X and Y. Its midpoint is then pulled taut to a point A above XY, and then to a point B below XY. Formulate a proof using triangle congruence to justify that the line AB is the perpendicular bisector of XY.

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hard

Describe in detail the steps to copy a given angle,

\angle PQR

, onto a new ray, MN. Explain the geometric principle that guarantees the new angle is congruent to the original.

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hard

Design a complex geometric pattern that is constructible using only a ruler and compass. The design must start with a single line segment and must incorporate at least three of the following constructions: perpendicular bisector, angle bisection, construction of a

60^\circ

angle, and construction of a parallel line. Provide a clear, step-by-step description of how to create your design.

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hard

A tiler has an unlimited supply of identical, regular pentagonal tiles. Can they tile an entire flat floor without any gaps or overlaps? Evaluate this possibility and justify your reasoning.

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Constructions and TilingsClass 7 Mathematics Practice Questions