Construct Triangle When Its Base, Sum of the Other Two Sides and One Base Angle Are Given
Construct Δ P...
Construct ΔPQR, given ¯¯¯¯¯¯¯¯PQ=3.5cm,¯¯¯¯¯¯¯¯PR=3cm, and ∠RPQ=120∘
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Construct ∠XPQ=120∘ with your compass.
With P as centre, draw an arc with radius equal to 3 cm that intersects ¯¯¯¯¯¯¯¯¯XP at point R.
PQR is the required triangle.
Thus, we see that if two sides of a triangle are given and the measure of the angle between these two sides is also given, then we can construct a triangle. This is known as SAS criterion for construction of triangles.