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Construction of Triangle When the Lengths of Two Sides and the Measure of
Included Angle are given (SAS Criterion)

Let us learn the construction of a triangle when the lengths of two sides and the measure of included

angle are given, i.e., SAS criterion.
Example 6: Construct a DABC in which AB = 3 cm, BC = 5.5 cm and ∠ABC = 60°.
A
Solution: Draw a rough skectch of DABC with given measures, this
will help us decide how to proceed. 3 cm

Steps of construction: 60°
1. Draw a line segment BC of length 5.5 cm. 5.5 cm
Rough Sketch
2. At B, construct ∠DBC = 60° with BC as base.
3. Now, with B as centre, draw an arc of radius 3 cm. It
cuts BD at point A.

4. Join AC. Thus, DABC is the required triangle.

A Pinch of History
The Sulba Sutras, ancient Indian texts dating back to around 800–500
BCE, laid the foundations of geometry, especially in constructing altars
for religious rituals. Baudhayana, one of the most prominent authors of
these texts, described methods to construct a circle nearly equal in area
to a square, and vice versa. In Sutras I-58 and I-59, he detailed procedures
for this, demonstrating an understanding of approximating the relationship between the areas
of squares and circles. His work, likely driven by the need to create circular altars, included
constructing circles that circumscribed squares, contributing significantly to ancient geometry.
Construction of a Triangle when the Measure of Two of its Angles and Included

Side are given (ASA Criterion)

Now, we will learn the construction of a triangle when the measure A
of two of its angles and included side are given, i.e., ASA criterion.

Example 7: Construct a triangle ABC such that BC = 6.3 cm, ∠B = 45°,
and ∠C = 60° using ruler and compasses only.

Solution: Draw a rough sketch of DABC with measures marked on 45° 60°
B C
it, this will help us decide how to proceed. 6.3 cm
Rough Sketch
Steps of construction:
1. Draw a line segment BC of length 6.3 cm. A
2. At B, construct ∠PBC = 45°.

3. At C, construct ∠BCQ = 60°.
4. Let rays BP and CQ intersect at A. 45° 60°
Thus, DABC is the required triangle. B 6.3 cm C

347 Construction of Basic Geometrical Shapes