Question

Construct $\Delta PQR$, given $\overline{PQ}=3.5cm,\overline{PR}=3cm$, and $\angle RPQ={120}^{\circ }$

Answer 1

Draw $\overline{PQ}=3.5cm$

Construct $\angle XPQ={120}^{\circ }$ with your compass.

With P as centre, draw an arc with radius equal to 3 cm that intersects $\overline{XP}$ at point R.

Join $\overline{RQ}$

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.