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**Proof of Theorem 6.7 :** If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

**Proof of Pythagoras Theorem (Theorem 6.8 ):** In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

**Proof of converse of Pythagoras Theorem (Theorem 6.9) :** In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.