State :
Converse of Pythagoras theorem.

State : Pythagoras theorem.

State : Converse of Thales theorem.

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x) = x^(2)-1 " for "x in [1, 2] .

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.]

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.

Converse of prArrq is …… .