Using vectors,prove that angle in a semi circle is a right angle.

A wavefront is defind as a surface of constant phase.Using Huygen.s Principle, prove that angle of incidence is equal to angle of reflection.

Consider the triangle with vertices A (4,4),B (3,5) and C (-1,-1) Using pythagoras theorem prove that Delta ABC is right angled.

Let A (0,4,1), B(2,3,-1) and C(4,5,0) be the vertices of a DeltaABC .Prove that DeltaABC is isosceles and right angled

If veca,vecb,veca+vecb are unit vectors, then prove that the angle between veca and vecb is (2pi)/(3)

In triangle 'ABC, angle B=90 degree . BD' is perpendicular to 'AC'. a) If 'angle A=x degree', find the measures of 'angle C' and 'angle ABD' b) Write the ratios of the sides opposite to the equal angles in triangle 'ABD' and triangle ABC. c) Prove that 'AB^2=AD x AC'.