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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 7. The content follows the official curriculum structure and exam pattern.

Constructions — Class 7 ICSE (2025-26)

About Constructions — Class 7 ICSE

Construct parallel lines, triangles, and angles using ruler and compass. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 18). On this page you can practice 60 questions across three difficulty levels — 20 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 & Tools
Constructing Angles and Bisectors
Constructing Perpendicular Lines and Perpendicular Bisectors
Constructing Parallel Lines
Constructing Triangles (SSS, SAS, ASA)

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

Constructions — solved examples for Class 7 ICSE

Example 1easy

Which of the following statements is TRUE about the perpendicular bisector of a line segment?

A)It divides the line segment into two unequal parts.
B)It passes through one endpoint of the line segment.
C)It is perpendicular to the line segment and divides it into two equal parts.
D)It makes an acute angle with the line segment.

Step-by-step solution

A perpendicular bisector, by definition, has two key properties.
First, it is perpendicular to the given line segment, meaning it forms a 90° angle with it.
Second, it bisects the line segment, meaning it divides it into two parts of equal length.
Therefore, the statement 'It is perpendicular to the line segment and divides it into two equal parts' accurately describes a perpendicular bisector.

Answer: It is perpendicular to the line segment and divides it into two equal parts.

Example 2medium

Which pair of tools is fundamental for performing geometric constructions accurately using only a straightedge and compass?

A)A) Protractor and Ruler
B)B) Set-squares and Divider
C)C) Ruler and Compass
D)D) Scale and Eraser

Step-by-step solution

Geometric constructions, by definition, rely solely on two primary tools: an unmarked straightedge (ruler) for drawing straight lines and a compass for drawing arcs and circles of specific radii.
Other tools like protractors or set-squares are used for drawing or measuring, but not for 'constructions' in the strict classical sense of using only compass and straightedge.

Answer: C) Ruler and Compass

Example 3hard

When constructing a line parallel to a given line 'l' through an external point 'P' by copying an angle (e.g., corresponding angles), which fundamental geometric axiom or theorem is being applied to guarantee the constructed line is indeed parallel?

A)A) Angle Sum Property of a Triangle
B)B) SAS Congruence Criterion
C)C) Converse of Corresponding Angles Axiom
D)D) Perpendicular Bisector Theorem

Step-by-step solution

The construction method involves creating an angle equal to a corresponding angle on the transversal.
The Converse of Corresponding Angles Axiom states that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel.
Therefore, by constructing equal corresponding angles, we are directly applying this axiom to ensure parallelism.

Answer: C) Converse of Corresponding Angles Axiom

Practice questions on Constructions

Q1.easy
Rohan wants to construct an angle of 60° using a ruler and compass. He drew a ray AB. What should be his NEXT step?
1. A)Draw an arc from point B with any radius, intersecting AB at C.
2. B)Draw an arc from point A with any radius, intersecting AB at C.
3. C)Draw a line perpendicular to AB from point A.
4. D)Draw a line parallel to AB from a point outside the ray.
Show answer
Answer: Draw an arc from point A with any radius, intersecting AB at C.
Hint: Think about where the center of the first arc should be when constructing a standard angle like 60°.
Q2.easy
To construct a parallel line to a given line 'l' through a point 'P' not on 'l', which of the following angle pairs can be used to ensure parallelism?
1. A)Only vertically opposite angles.
2. B)Only adjacent angles.
3. C)Only corresponding angles or alternate interior angles.
4. D)Only linear pair angles.
Show answer
Answer: Only corresponding angles or alternate interior angles.
Hint: Recall the conditions involving a transversal intersecting two lines that guarantee the lines are parallel.
Q3.easy
An angle bisector of ∠ABC is a ray BD such that:
1. A)BD is perpendicular to AC.
2. B)∠ABD = ∠CBD.
3. C)BD passes through the midpoint of AC.
4. D)∠ABD + ∠CBD = 180°.
Show answer
Answer: ∠ABD = ∠CBD.
Hint: The term 'bisector' implies dividing something into two equal parts.
Q4.medium
To construct an angle of 60° at a point on a given ray, after drawing an initial arc from the point that cuts the ray, how many additional arcs (from the intersection point on the ray) are needed to mark the 60° point?
1. A)A) 1
2. B)B) 2
3. C)C) 3
4. D)D) 4
Show answer
Answer: A) 1
Hint: Remember the fundamental steps for constructing a 60° angle using a compass.
Q5.medium
When constructing a line parallel to a given line 'l' through an external point 'P', which property of lines and transversals is most commonly used to ensure parallelism?
1. A)A) Sum of angles on a straight line is 180°
2. B)B) Vertically opposite angles are equal
3. C)C) Corresponding angles are equal
4. D)D) Angles in a linear pair are supplementary
Show answer
Answer: C) Corresponding angles are equal
Hint: Think about how you transfer an angle from the given line to the external point to create the parallel line.
Q6.medium
To construct the perpendicular bisector of a line segment AB, what is the *first* essential step after drawing the segment AB?
1. A)A) Draw a line through A
2. B)B) With A as centre, draw an arc with radius greater than half of AB
3. C)C) With A as centre, draw an arc with radius equal to AB
4. D)D) Draw a circle with AB as diameter
Show answer
Answer: B) With A as centre, draw an arc with radius greater than half of AB
Hint: The perpendicular bisector construction involves intersecting arcs from both endpoints.
Q7.hard
A student performs a sequence of constructions: 1. Constructs a 90° angle. 2. Bisects this 90° angle. 3. Constructs a 60° angle such that it shares one arm with one of the 45° angles obtained in step 2, and the 60° angle is formed on the *exterior* side of that 45° angle. What is the measure of the total angle formed by the two outermost rays of the entire construction?
1. A)A) 105°
2. B)B) 120°
3. C)C) 135°
4. D)D) 150°
Show answer
Answer: A) 105°
Hint: Break down the steps and visualize the angles being formed. When the 60° angle is formed on the 'exterior side', it means it extends beyond the original 90° angle in one direction, or adds to the 45° section.
Q8.hard
A designer proposes a triangular garden bed with sides measuring 5 cm, 7 cm, and 13 cm. Using only a ruler and compass, can this triangular garden bed be accurately constructed?
1. A)A) Yes, because all side lengths are positive.
2. B)B) No, because the sum of the two shorter sides is not greater than the longest side.
3. C)C) Yes, because a unique triangle can always be constructed with three given sides.
4. D)D) No, because 13 is not a multiple of 5 or 7.
Show answer
Answer: B) No, because the sum of the two shorter sides is not greater than the longest side.
Hint: Recall the Triangle Inequality Theorem, which specifies a fundamental condition for any three segments to form a triangle.
Q9.hard
You are given a line segment AB. To find a point C that is equidistant from A and B using only a ruler and compass, which construction should you perform, and why does it guarantee equidistance?
1. A)A) Draw a circle with center A and radius AB. C will be on the circle.
2. B)B) Construct the angle bisector of ∠A.
3. C)C) Construct the perpendicular bisector of AB. Any point on it is equidistant from A and B.
4. D)D) Draw a line parallel to AB through an external point.
Show answer
Answer: C) Construct the perpendicular bisector of AB. Any point on it is equidistant from A and B.
Hint: Consider the definition and properties of the perpendicular bisector of a line segment. What is special about points on it?

These are 9 of the 60 questions available for Constructions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.