Concepts A triangle which has two of its sides equal is called an isosceles triangle Properties of Isosceles Triangle 1. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle. 2. The side opposite the vertex angle is called the base and base angles are equal. 3. The perpendicular from the vertex angle bisects the base and the vertex angle. Both triangle QPS and QSR are isosceles triangles (have two sides equal and hence 2 angles equal) For triangle QSR ∠SQR=∠QRS=35∘ But angles in a triangle add up to 180∘ ⇒∠SQR+∠QRS+∠RSQ=180 ⇒35+35+∠RSQ=180 70+∠RSQ=180 ∠RSQ=180−70 ∠RSQ=110∘ For triangle QPS ∠RSQ+∠QSP=180 (Angles on a straight line add up to 180∘ But ∠RSQ=110∘ ⇒110+∠QSP=180 ∠QSP=180−110 ∠QSP=70 Angles in a triangle add up to 180∘ ⇒∠SQP+∠QSP+∠QPS=180 ∠SQP=∠QSP=70 ⇒70+70+∠QPS=180 ⇒140+∠QPS=180 ⇒∠QPS=180−140 ∠QPS=40∘