# Isosceles Triangles and Their Applications

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If any two sides of a triangle are equal, the triangle is said to be an isosceles triangle.

If two sides of a triangle are equal, the angles opposite to them are also equal.

If two angles of a triangle are equal, the sides opposite to them are also equal.

The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle.

Altitude of a triangle is a perpendicular distance from the base to the top most vertex of a triangle.

The bisector of the angle at the vertex of an isosceles triangle bisects the base at right angles.

If equal sides of an isosceles triangle are produced, the exterior angles so formed are equal.

The perpendicular bisector of the base of an isosceles triangle passes through the vertex of the triangle.

The line joining the midpoint of the base of an isosceles triangle and the opposite vertex is perpendicular to the base and bisects the angle at the vertex.

When the 3rd angle of an isosceles triangle is a right angle, it is called a “right isosceles triangle”.

The shape of an isosceles triangle is used in designing buildings.

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