How to Solve Geometric Constructions — Step by Step Guide

Construct angles, triangles and bisectors using a compass and straightedge. This guide covers Class 9 to 10.

Step-by-Step Method

  1. 1

    Always use a sharp pencil and a compass that holds its radius firmly.

  2. 2

    To bisect a line segment: open the compass to more than half the length, draw arcs from both endpoints. The line through the intersection points is the perpendicular bisector.

  3. 3

    To bisect an angle: draw an arc from the vertex cutting both rays, then draw arcs from both intersection points. The line from the vertex through the new intersection bisects the angle.

  4. 4

    To construct a triangle given SSS: draw the base first, then use the compass to mark the other two sides as arcs. Their intersection gives the third vertex.

  5. 5

    For SAS: draw the base, construct the given angle at one end, mark the given side length on the ray.

Worked Example

Problem: Construct an angle of 60° using a compass.

Solution: Draw a ray. With the compass, draw an arc from the endpoint. Keep the same radius, place the compass at the point where the arc meets the ray, and draw another arc intersecting the first. Join the endpoint to this intersection to get a 60° angle.

Common Mistakes to Avoid

  • ✗

    Changing the compass width accidentally during a construction.

  • ✗

    Not drawing arcs large enough to intersect clearly.

  • ✗

    Erasing construction lines — they should be shown as part of the answer.

  • ✗

    Using a protractor when only a compass and straightedge are allowed.

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Frequently Asked Questions

How do I solve Geometric Constructions problems?
Always use a sharp pencil and a compass that holds its radius firmly. To bisect a line segment: open the compass to more than half the length, draw arcs from both endpoints. The line through the intersection points is the perpendicular bisector.
What are common mistakes in Geometric Constructions?
Changing the compass width accidentally during a construction. Not drawing arcs large enough to intersect clearly.
Which class covers Geometric Constructions?
Geometric Constructions is typically taught in Class 9, 10. SparkEd has free practice for all these grades.
Where can I practise Geometric Constructions for free?
SparkEd offers free chapter-wise practice for Geometric Constructions aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

SparkEd Maths — sparked.coms@gmail.com — www.sparkedmaths.com