Question

Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.

Answer 1

Let ABC be the triangle and BC is its base. Let AD be the line joining A to BC Given ABC is an isosceles triangle hence line joining the vertex to any point on its base is 90° Here ΔABD and ΔADC are right angled triangles Here AB and AC are the hypotenuses of ΔABD and ΔADC Recall that hypotenuse is greater than any of the sides of triangle Hence AB > AD and also AC > AD