Question

the straight line joining the vertex of an isosceles triangle to any point on 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

Answer 2

The mathematical study of isosceles triangles dates back to ancient Egyptian mathematicsand Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two