Mathematics Notes for Class 10 Constructions

Constructions

Welcome to the chapter on Constructions for Class 10. In this chapter, you will learn how to draw geometric shapes and figures accurately using a ruler and compass. By the end of this chapter, you will be able to construct angles, triangles, tangents to circles, and more, following mathematical rules.

Key Concepts

Construction: Drawing shapes, angles, and lines accurately using only a ruler and compass.
Bisector: A line that divides an angle or a segment into two equal parts.
Tangent: A line that touches a circle at exactly one point.

Basic Constructions

Bisecting a given angle
Bisecting a given line segment
Constructing a perpendicular to a line from a point on or outside the line
Constructing angles of 30°, 45°, 60°, 90°, and 120°

Construction of Triangles

Constructing a triangle when lengths of all three sides are given (SSS)
Constructing a triangle when two sides and the included angle are given (SAS)
Constructing a triangle when two angles and the included side are given (ASA)
Constructing a triangle similar to a given triangle as per a given scale factor

Construction of Tangents to a Circle

Constructing a tangent to a circle from a point outside the circle
Constructing tangents from a point on the circle

Steps of Construction

Each construction problem should be solved step by step. Always use a sharp pencil, a ruler, and a compass. Write the steps clearly and label all points.

Practice Questions

Construct an angle of 90° at a given point on a line.
Bisect a given line segment of 8 cm.
Construct a triangle with sides 5 cm, 6 cm, and 7 cm.
Construct a triangle similar to a given triangle with a scale factor of 3:2.
Draw a circle of radius 4 cm and construct a tangent from a point 7 cm away from its center.

Challenge Yourself

Construct a triangle with sides 6 cm, 8 cm, and 10 cm and then construct its incircle.
Given a triangle, construct another triangle whose sides are 2/3 of the corresponding sides of the given triangle.

Did You Know?

Constructions are used in real life for making designs, buildings, and maps.
Ancient mathematicians used only a compass and straightedge for constructions—no measurements!

Glossary

Compass: A tool used to draw circles and arcs.
Straightedge: A ruler without markings, used to draw straight lines.
Scale Factor: The ratio by which a figure is enlarged or reduced.

Answers to Practice Questions

Use compass and ruler to construct a 90° angle at the given point (draw a semicircle, mark points, and join).
Open compass to more than half the segment, draw arcs from both ends, and join intersection points to bisect.
Draw base 6 cm, use compass to mark 5 cm and 7 cm arcs from ends, join to form triangle.
Draw the given triangle, use parallel lines and scale factor to construct the similar triangle.
Draw the circle, mark the external point, join center to point, construct perpendicular at the point of contact for tangent.

Practice constructions to improve your geometry skills and accuracy!

Mathematics Class 10 - Constructions Notes