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We know how to construct a triangle when \(3\) sides are known. Now, let us learn how to construct a triangle when \(2\) sides and an angle are known and also how to construct a triangle when \(1\) side and \(2\) angles are known.
1. Construction of a triangle when \(2\) sides and the included angle
Let us understand the construction using an example.
Example:
Consider a triangle \(ABC\) with measurements \(AB = 4 \ cm\), \(BC = 6 \ cm\) and \(\angle ABC = 120^{\circ}\).
Construction:
Step 1: Draw a base line segment \(BC = 6 \ cm\).
Step 2: Using a protractor, construct \(\angle B = 120^{\circ}\) by drawing the other arm of the triangle.
Step 3: With \(B\) as centre and \(4 \ cm\) as radius, draw an arc which cuts the arm at \(A\).
Step 4: Join \(AC\).
Thus, \(ABC\) is the required triangle.
2. Construction when \(2\) angles and the included side
Let us understand the construction using an example.
Example:
Construct a triangle \(ABC\) with measurements \(AB = 8 \ cm\), \(\angle CAB = 60^{\circ}\) and \(\angle ABC = 40^{\circ}\).
Construction:
Step 1: Draw a base line segment \(AB = 8 \ cm\).
Step 2: Place the protractor at \(A\) and construct \(\angle XAB = 60^{\circ}\).
Step 3: Place the protractor at \(B\) and construct \(\angle YBA = 40^{\circ}\).
Step 4: Mark the intersecting point of the two arms as the vertex \(C\).
Thus, \(ABC\) is the required triangle.
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