The angles opposite to equal sides of a triangle are equal. The sides opposite to equal angles of a triangle are equal.

Perpendiculars or altitudes drawn on equal sides, from opposite vertices of an isosceles triangle are equal.

If two sides of a triangle are unequal, then the longer side has the greater angle opposite to it. In a triangle, the greater angle has longer side opposite to it. Sum of any two sides of a triangle is greater than the third side.

If a line drawn **parallel to one side of a triangle** intersects the other two sides at distinct points, the other two sides of the triangles are divided proportionally. If a line divides any two sides of a triangle in the same ratio, the line is parallel to third side of the triangle.

The **internal bisector of any angle** of a triangle divides the opposite side in the ratio of sides containing the angle.

If a perpendicular is drawn from the vertex containing right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to each other and to the original triangle.

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

**Pythagoras Theorem:** In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.