Maharashtra Board Practice Worksheet
Class 10 Maths 2 Chapter 4
Geometric Constructions Worksheet
Practise Maharashtra Board Class 10 Maths 2 Chapter 4 Geometric
Constructions with MCQs, construction steps, proportional division,
similar triangles, tangents and board-exam-style questions.
Worksheet objective: Develop accuracy in compass-and-ruler
constructions, write every construction step in the correct order and
preserve all required arcs in the final diagram.
Class 10 Geometric Constructions Worksheet
This Geometric Constructions worksheet is designed for Maharashtra
State Board students who want structured practice after studying
Chapter 4. It includes questions on dividing a line segment in a given
ratio, constructing triangles similar to a given triangle and drawing
tangents to a circle.
Construction questions require more than a correct final figure.
Students must draw the necessary rays and arcs, label every point
clearly and write the steps in a logical sequence. The worksheet helps
students practise both the diagram and its written construction.
÷
Divide a Line Segment
Divide a given segment internally in the required ratio using
equal arcs and parallel lines.
△
Similar Triangles
Construct a triangle similar to a given triangle according to
the stated scale factor.
○
Tangents to a Circle
Construct tangents from a point on or outside a circle using
accurate compass arcs.
Concepts Covered in the Worksheet
Division of a Line Segment
Students divide a line segment in a given ratio by drawing an
auxiliary ray, marking equal parts with a compass and constructing
a line parallel to the required joining segment.
Construction of Similar Triangles
These questions require students to construct an enlarged or
reduced triangle using a given scale factor. The corresponding
sides must remain proportional.
Tangent at a Point on a Circle
Students join the centre to the point of contact and construct a
line perpendicular to that radius. The perpendicular line is the
required tangent.
Tangents from an External Point
Students join the centre to the external point, locate the
midpoint, draw an auxiliary circle and identify the points of
contact before drawing both tangents.
Board-Exam Construction Questions
Mixed questions assess the accuracy of the figure, visible
construction arcs, correct labels and the written sequence of
construction steps.
How to Complete a Construction Question
- Read the measurements, ratio or scale factor carefully.
- Draw the given line segment, triangle or circle accurately.
- Label every given point before continuing the construction.
- Use a sharp pencil, compass and ruler for clear arcs and lines.
- Keep the compass width unchanged when equal arcs are required.
- Draw auxiliary rays and construction arcs lightly but visibly.
- Join the required points only after verifying their positions.
- Write the construction steps in the same order as the diagram.
Important Instructions for Accurate Diagrams
- Do not erase the arcs used to locate construction points.
- Use the given measurements and ratios exactly.
- Label every point clearly and consistently.
- Do not estimate a midpoint or perpendicular by appearance.
- Use a compass to transfer equal lengths.
- Use a ruler only for drawing straight lines, not measuring arcs.
- Show the auxiliary circle when constructing external tangents.
- Check that the tangent meets the circle at only one point.
Benefits of Practising This Worksheet
- Improves compass-and-ruler accuracy.
- Develops confidence in proportional constructions.
- Provides practice in enlargement and reduction of triangles.
- Improves understanding of tangent construction.
- Develops clear labelling and diagram presentation.
- Helps students write construction steps in logical order.
- Supports school tests, prelims and SSC Board preparation.
Common Mistakes Students Should Avoid
- Do not erase the important construction arcs.
- Do not change the compass width while marking equal parts.
- Do not divide the segment by visual estimation.
- Do not use an incorrect scale factor for a similar triangle.
- Do not draw a tangent without constructing the perpendicular.
- Do not forget to mark the centre and point of contact.
- Do not leave important construction points unlabelled.
- Do not write steps that are missing from the diagram.
Check Your Work with Chapter 4 Solutions
Attempt every construction independently and preserve all required
arcs. After completing the worksheet, compare your diagrams and written
steps with the complete Chapter 4 Geometric Constructions solutions.
View Chapter 4 Solutions →
Frequently Asked Questions
Select any question to view its answer.
What topics are covered in this worksheet?
It covers proportional division, similar-triangle construction,
tangents at a point and tangents from an external point.
Which instruments are required?
Students require a sharp pencil, ruler, compass and eraser.
Should construction arcs be erased?
No. Important construction arcs should remain visible because
they show how the required points were obtained.
How is a line segment divided in a given ratio?
Draw an auxiliary ray, mark equal parts, join the last point to
the segment endpoint and draw the required parallel line.
How is a tangent drawn at a point on a circle?
Join the centre to the given point and construct a perpendicular
to the radius at that point.
Why must the compass width remain unchanged?
An unchanged compass width ensures that the marked segments or
arcs are equal.
Does this worksheet include board-exam questions?
Yes. It includes construction questions suitable for school
tests, prelims and Maharashtra SSC Board preparation.
When should I check the solutions?
Check the solutions after completing the construction and
writing all steps independently.
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