State :
Pythagoras theorem.

State : Converse of Pythagoras theorem.

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Without using the Pythagoras theorem, show that the points (4,4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Without using Pythagoras theorem prove that A(12, 8), B(-2, 6) and C(6, 0) are the verticies of right angled triangle.

Without using pythagoras theorem, show that the points A(-1,3) ,B(0,5) and C(3,1) are the vertices of a right angled triangle

In the given figure, AB = 36 cm and M is the midpoint of AB. Semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of shaded region. [Hint : Take O as the centre of semicircle on diameter AM. Take the radius of the circle with centre C as r. Then , OC = (9 + r)cm, OM = 9 cm and CM = (18-r) cm. Now, use Pythagoras theorem and find r = 6 cm.]

State and prove theorem of perpendicular axes.

State and prove theorem of parallel axis.

Write carnot theorem.

Envied by the popularity of Pythagoras his disciple claimed a different relation between the sides of right angle triangles. By observing this what do you notice?