Lines and Triangles

If $$S$$ is any point in the interior of $$\Delta PQR$$, prove that $$(SQ + SR) < (PQ + PR)$$.
In $$\Delta ABC, \, \angle A = 90^o , \, AB = 5$$ cm and $$BC = 13 $$ cm. Find the radius of the incircle of $$\Delta ABC$$.
The sides of a triangle are $$6$$ cm, $$11$$ cm and $$15$$ cm. Construct incircle and find the radius of the triangle.
In right triangle ABC, the right angle is at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point) B (see figure). 
When we write $$\angle A = \angle B$$ , we actually mean ______________.