Pythagoras Theorem

Pythagoras theorem : In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides.

Pythagorean Triplet : In a triplet of natural numbers, if the square of the largest number is equal to the sum of the squares of the remaining two numbers then the triplet is called Pythagorean triplet. For Example: In the triplet ( 11, 60, 61 )

Property of 30°-60°-90° triangle. If acute angles of a right angled triangle are 30° and 60°, then the side opposite 30°angle is half of the hypotenuse and the side opposite to 60° angle is root 3 times the side opposite 30°angle

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Similarity and right angled triangle Theorem :In a right angled triangle, if the altitude is drawn to the hypotenuse, then the two triangles formed are similar to the original triangle and to each other

Theorem of geometric mean In a right angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex, is the geometric mean of the segments into which the hypotenuse is divided.

Converse of Pythagoras Theorem: In a triangle, if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right angled triangle

In a right angled triangle, if one side is half of the hypotenuse then the angle opposite to that side is 30°. This property is the converse of 30°-60°-90° theorem.