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SparkEd Math offers 60+ practice questions for Constructions across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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SparkEd Math uses visual step-by-step solutions for every Constructions problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Constructions content aligned with the ICSE syllabus?

Yes, all Constructions questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Constructions — Class 8 ICSE (2025-26)

About Constructions — Class 8 ICSE

Construct quadrilaterals given specific side, angle, and diagonal measurements. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 16). On this page you can practice 50 questions across three difficulty levels — 10 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Constructions

Introduction to Geometric Constructions
Foundation: Constructing Triangles
Constructing General Quadrilaterals
Constructing Quadrilaterals with Angles and Special Cases
Advanced Constructions and Problem-Solving

Interactive lesson · about 15 minutes · checkpoint question after every unit

Constructions — solved examples for Class 8 ICSE

Example 1easy

What is the minimum number of independent measurements required to construct a unique general quadrilateral?

Step-by-step solution

A quadrilateral can be divided into two triangles by a diagonal.
Each triangle requires 3 independent measurements (e.g., SSS, SAS, ASA).
For a quadrilateral, you typically need 4 sides and 1 diagonal, or 3 sides and 2 diagonals, or 2 adjacent sides and 3 angles, or 3 sides and 2 included angles.
In all these cases, the total count of independent measurements is 5.

Answer: 5

Example 2medium

To construct a quadrilateral ABCD where AB = 5 cm, BC = 6 cm, CD = 4 cm, DA = 7 cm, and diagonal AC = 8 cm, what is the *first* step after drawing the initial base line segment AB?

A)Draw an arc with center B and radius 6 cm.
B)Draw an arc with center A and radius 7 cm.
C)Draw an arc with center A and radius 8 cm.
D)Draw an arc with center C and radius 4 cm.

Step-by-step solution

Draw the base line segment AB = 5 cm.
To locate point C, you need AC and BC. You have AC = 8 cm and BC = 6 cm.
Therefore, the first step after drawing AB to find C is to draw an arc with center A and radius AC = 8 cm. Subsequently, an arc from B with radius BC = 6 cm would intersect it to define C.

Answer: Draw an arc with center A and radius 8 cm.

Example 3hard

Which of the following sets of measurements is NOT sufficient to construct a unique parallelogram?

A)Two adjacent sides and one angle.
B)Two adjacent sides and one diagonal.
C)Both diagonals and the angle between them.
D)All four sides.

Step-by-step solution

A parallelogram is defined by its opposite sides being equal and parallel. If all four sides are given, it means only two distinct adjacent side lengths are given (e.g., AB=CD and BC=DA). This is equivalent to giving two adjacent sides.
To construct a unique parallelogram, we typically need 3 independent measurements (e.g., two adjacent sides and an included angle, or two sides and a diagonal). Giving all four sides only provides two distinct lengths, which is insufficient to fix the angles or diagonals.
For example, you can construct multiple parallelograms with the same side lengths but different angles (e.g., a rhombus and a square, or a parallelogram and a rectangle with same side lengths).

Answer: All four sides.

Practice questions on Constructions

Q1.easy
When constructing a 60° angle using a compass and ruler, after drawing a ray, what is the immediate next step?
1. A)Draw an arc from the endpoint of the ray, intersecting the ray.
2. B)Place the protractor at the endpoint and mark 60°.
3. C)Draw a line perpendicular to the ray.
4. D)Measure a 60 mm segment on the ray.
Show answer
Answer: Draw an arc from the endpoint of the ray, intersecting the ray.
Hint: Think about how equilateral triangles are formed using a compass. The first arc sets the radius for subsequent steps.
Q2.easy
When constructing a quadrilateral ABCD given the lengths of all four sides (AB, BC, CD, DA) and one diagonal (AC), why is it a common practice to first construct two triangles?
1. A)It helps to align the angles correctly.
2. B)It's impossible to construct a quadrilateral directly with just sides and one diagonal.
3. C)A diagonal divides any quadrilateral into two triangles, each constructible by SSS criterion.
4. D)This method requires fewer tools than other methods.
Show answer
Answer: A diagonal divides any quadrilateral into two triangles, each constructible by SSS criterion.
Hint: Consider how a quadrilateral can be decomposed into simpler shapes that you already know how to construct.
Q3.easy
To construct a unique rhombus, if you are given the length of one side and the length of one diagonal, how many *additional* independent measurements do you need?
1. A)0
2. B)1
3. C)2
4. D)3
Show answer
Answer: 0
Hint: Remember the defining property of a rhombus concerning its sides.
Q4.medium
Raj is constructing a quadrilateral PQRS where PQ = 6 cm, QR = 4.5 cm, ∠P = 75°, ∠Q = 105°, and ∠R = 120°. After drawing PQ and constructing ∠P and ∠Q, what should be the *next* logical step to locate point R?
1. A)Draw an arc with center P and radius PR.
2. B)Draw a line segment from Q making an angle of 105° and measure QR = 4.5 cm along it.
3. C)Draw a line segment from Q making an angle of 120°.
4. D)Draw an arc with center R and radius RS.
Show answer
Answer: Draw a line segment from Q making an angle of 105° and measure QR = 4.5 cm along it.
Hint: You've constructed the base and two angles. Now use the given side QR and the angle at Q.
Q5.medium
To construct a quadrilateral EFGH where EF = 6 cm, FG = 5 cm, GH = 4 cm, ∠F = 90°, and ∠G = 60°, which of the following statements correctly describes the initial setup?
1. A)Draw EF = 6 cm, then construct ∠F = 90° at F, and then construct ∠G = 60° at G.
2. B)Draw FG = 5 cm, then construct ∠F = 90° at F, and then construct ∠G = 60° at G.
3. C)Draw GH = 4 cm, then construct ∠G = 60° at G, and then construct ∠F = 90° at F.
4. D)Draw EF = 6 cm, then construct ∠G = 60° at G, and then construct ∠F = 90° at F.
Show answer
Answer: Draw FG = 5 cm, then construct ∠F = 90° at F, and then construct ∠G = 60° at G.
Hint: When two included angles are given, it's often easiest to start with the side that is *between* those two angles.
Q6.medium
To construct a parallelogram ABCD with AB = 7 cm, AD = 5 cm, and diagonal AC = 9 cm, which property of a parallelogram is most directly used to complete the construction *after* constructing triangle ABC?
1. A)Opposite angles are equal.
2. B)Diagonals bisect each other.
3. C)Opposite sides are equal in length.
4. D)Adjacent angles are supplementary.
Show answer
Answer: Opposite sides are equal in length.
Hint: After constructing the first triangle (ABC), you need to locate the fourth vertex (D). How do the side lengths of a parallelogram relate?
Q7.hard
A student attempts to construct an angle of 75° using only a compass and ruler. Which of the following sequences of angle constructions is the most efficient and correct?
1. A)Construct 60°, then bisect it to get 30°, then add 30° to 60°.
2. B)Construct 90°, then bisect it to get 45°, then add 30° to 45°.
3. C)Construct 60° and 90°, then bisect the angle between them (30°) to get 15°, then add 15° to 60°.
4. D)Construct 120°, then bisect it to get 60°, then bisect 60° to get 30°, then add 30° to 60°.
Show answer
Answer: Construct 60° and 90°, then bisect the angle between them (30°) to get 15°, then add 15° to 60°.
Hint: Remember that 75° can be expressed as a sum or difference of commonly constructible angles. Think about angles that are easy to construct (like 60° and 90°) and how you can combine them or bisect their difference.
Q8.hard
Which of the following conditions is *impossible* for constructing a quadrilateral ABCD?
1. A)AB = 4 cm, BC = 6 cm, CD = 5 cm, DA = 7 cm, ∠A = 90°
2. B)AB = 3 cm, BC = 4 cm, CD = 5 cm, DA = 15 cm, ∠B = 60°
3. C)AB = 5 cm, BC = 5 cm, CD = 5 cm, DA = 5 cm, AC = 8 cm
4. D)AB = 6 cm, BC = 7 cm, AC = 10 cm, BD = 9 cm, ∠A = 70°
Show answer
Answer: AB = 3 cm, BC = 4 cm, CD = 5 cm, DA = 15 cm, ∠B = 60°
Hint: Consider the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Apply this to the triangles formed within the quadrilateral.
Q9.hard
You are given a task to construct a square with a diagonal of length 8 cm. Which of the following statements correctly describes a crucial initial step?
1. A)Draw a line segment of 8 cm. Bisect it at 90° and extend the bisector to 4 cm on each side.
2. B)Draw a line segment of 4 cm. At its endpoint, construct a 90° angle and mark 4 cm along it.
3. C)Draw a line segment of 8 cm. From its endpoints, draw arcs of 8 cm to find the vertices.
4. D)Construct a 90° angle. Mark 4 cm on both arms and connect the endpoints.
Show answer
Answer: Draw a line segment of 8 cm. Bisect it at 90° and extend the bisector to 4 cm on each side.
Hint: Recall the properties of a square's diagonals: they are equal, bisect each other at right angles. How can you use these properties to start your construction with the given diagonal length?

These are 9 of the 50 questions available for Constructions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.