How many practice questions are available for Practical Geometry?

SparkEd Math offers 60+ practice questions for Practical Geometry 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.

Is Practical Geometry content free on SparkEd Math?

Yes! All Practical Geometry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Practical Geometry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Practical Geometry 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 Practical Geometry content aligned with the ICSE syllabus?

Yes, all Practical Geometry questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 6. The content follows the official curriculum structure and exam pattern.

Practical Geometry — Class 6 ICSE (2025-26)

About Practical Geometry — Class 6 ICSE

Construct line segments, angles, perpendicular bisectors, and angle bisectors using compass and ruler. This topic is part of the ICSE Class 6 mathematics syllabus (chapter: Chapter 14). 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 Practical Geometry

Introduction to Practical Geometry & Line Segments
Constructing Perpendicular Bisectors
Constructing Basic Angles
Constructing Angle Bisectors
Summary, Connections & Exam Preparation

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

Practical Geometry — solved examples for Class 6 ICSE

Example 1easy

Which instrument is used to draw a circle of a given radius?

A)Ruler
B)Protractor
C)Compass
D)Set square

Step-by-step solution

A compass is a geometrical instrument with two arms.
One arm has a sharp point that is placed at the centre, and the other arm holds a pencil to draw the circle.
Therefore, a compass is used to draw a circle of a given radius.

Answer: Compass

Example 2medium

To construct an angle of 120 degrees using a compass, you construct a 60-degree angle and then:

A)Bisect the 60-degree angle
B)Construct another 60-degree angle adjacent to the first
C)Double the compass opening
D)Draw a perpendicular at the vertex

Step-by-step solution

First, construct a 60-degree angle using the standard compass method.
Then, from the point where the arc meets the first 60-degree arm, repeat the same construction to get another 60-degree angle.
The total angle = 60 + 60 = 120 degrees.

Answer: Construct another 60-degree angle adjacent to the first

Example 3hard

To construct a 75-degree angle using a compass and straightedge, which combination of constructions is used?

A)Construct 60 degrees and add 15 degrees (bisect 30 degrees)
B)Construct 90 degrees and subtract 15 degrees (bisect 30 degrees)
C)Both of the above
D)Construct 45 degrees and add 30 degrees

Step-by-step solution

Method 1: Construct 60 degrees and 30 degrees (bisect 60). Then bisect the 30-degree angle to get 15 degrees. Add: 60 + 15 = 75.
Method 2: Construct 90 degrees. Then construct 30 degrees from the 90-degree arm inward and bisect it to get 15 degrees. Subtract: 90 - 15 = 75.
Both methods are valid compass-and-straightedge constructions yielding 75 degrees.

Answer: Both of the above

Practice questions on Practical Geometry

Q1.easy
Which instrument is used to measure an angle?
1. A)Compass
2. B)Ruler
3. C)Protractor
4. D)Divider
Show answer
Answer: Protractor
Hint: This is a semi-circular instrument with degree markings from 0 to 180.
Q2.easy
To construct a line segment of length 5.6 cm, which pair of instruments is essential?
1. A)Compass and protractor
2. B)Ruler and compass
3. C)Protractor and set square
4. D)Divider and protractor
Show answer
Answer: Ruler and compass
Hint: You need one instrument to measure the length and another to mark it precisely.
Q3.easy
What is the first step in constructing a copy of a given line segment AB?
1. A)Draw any line and mark a point on it
2. B)Measure the length of AB using a protractor
3. C)Draw a circle with radius AB
4. D)Draw a perpendicular to AB
Show answer
Answer: Draw any line and mark a point on it
Hint: You need a base line and a starting point before you can copy the length.
Q4.medium
When constructing the perpendicular bisector of a line segment AB, the compass opening must be:
1. A)Exactly equal to AB
2. B)Less than half of AB
3. C)More than half of AB
4. D)Exactly half of AB
Show answer
Answer: More than half of AB
Hint: If the compass opening is too small, the arcs from A and B will not intersect.
Q5.medium
To construct a 30-degree angle using only a compass and straightedge, you should:
1. A)Construct a 60-degree angle and bisect it
2. B)Construct a 90-degree angle and trisect it
3. C)Construct a 45-degree angle and subtract 15 degrees
4. D)Directly draw arcs at 30 degrees
Show answer
Answer: Construct a 60-degree angle and bisect it
Hint: 30 is half of 60, and you know how to construct 60 degrees with a compass.
Q6.medium
In constructing a triangle with sides 4 cm, 5 cm, and 7 cm (SSS), after drawing the base of 7 cm, what is the next step?
1. A)Draw a perpendicular at one end of the base
2. B)With compass set to 4 cm, draw an arc from one end of the base
3. C)Measure and mark the midpoint of the base
4. D)Draw a 60-degree angle at one end
Show answer
Answer: With compass set to 4 cm, draw an arc from one end of the base
Hint: After drawing the base, you need to locate the third vertex using the other two sides.
Q7.hard
When constructing an equilateral triangle with compass and ruler, how many times do you use the same compass opening?
1. A)1
2. B)2
3. C)3
4. D)4
Show answer
Answer: 2
Hint: You draw the base with a ruler, then use the compass (set to the same length as the base) to find the third vertex.
Q8.hard
Point P lies on the perpendicular bisector of segment AB. If PA = 5 cm, what is PB?
1. A)2.5 cm
2. B)5 cm
3. C)10 cm
4. D)Cannot be determined
Show answer
Answer: 5 cm
Hint: Every point on the perpendicular bisector of a segment is equidistant from both endpoints.
Q9.hard
In the construction of a triangle with sides 6 cm, 8 cm, and 10 cm, the triangle formed is:
1. A)An acute-angled triangle
2. B)A right-angled triangle
3. C)An obtuse-angled triangle
4. D)An equilateral triangle
Show answer
Answer: A right-angled triangle
Hint: Check if the sides satisfy the Pythagorean relationship: does the square of the longest side equal the sum of squares of the other two?

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