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SAI International School
CLASS-VII
Mathematics
CHAPTER 7 A TALE OF THREE INTERSECTING LINES
Lesson Notes
SUBTOPIC: CONSTRUCTING TRIANGLES WITH ANGLES AND PROPERTIES
Introduction: Beyond Side-Based Construction
In earlier constructions, all three sides were known.
Now, we explore situations where angles are also involved.
This helps in constructing triangles when full side information is not available.
Case 1: Two Sides and the Included Angle
Concept
When two sides and the angle between them are given, a triangle can be constructed
uniquely.
The given angle determines the direction of the third vertex.
Construction Steps (Example)
Given: AB = 5 cm, AC = 4 cm, ∠A = 45°
1. Draw base AB = 5 cm
2. At point A, construct ∠A = 45°
3. On the angle arm, mark point C such that AC = 4 cm
4. Join BC
ΔABC is obtained
Diagram 1: Two Sides and Included Angle
Construction using two sides and the included angle (SAS method)
Observation
