theorem 1 1

If A and B are two invertible matrices of the same order, then (AB) - 1 = B - 1 A - 1..

The number of circular permutations of n different objects is (n-1)..

The length of the line segment AB, which joins A (x 1 , y 1 ) and B (x 2 , y 2 ) is given by ..

If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that In figure (i), A < 90 o But from D BAE, we have In figure (ii), A > 90 o But from D BAE, we hav..

Theorem 1 - In a polygon of 'n' sides, the sum of the interior angles is equal to (2n - 4) right angles. ABCDE is an n sided polygon. The sum of the interior angles = (2n - 4) right angles Take any point O inside the polygon. Join OA, OB, O..

Parallelograms on the same base and between the same parallels are equal in area. ABCD and ABEF are two parallelograms on the same base AB and between the same parallels AB, DE area (ABCD) = area (ABEF) An alternate way of proving this theorem is as follows: Since both parallelograms are ..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We sh..

Theorem 1 - If two sides of a triangle are equal, the angles opposite to them are equal. In AB = AC Draw AD, the bisector of to meet BC at ..

In a polygon of 'n' sides, the sum of the interior angles is equal to (2n - 4) right angles. ABCDE is an n sided polygon. The sum of the interior angles = (2n - 4) right angles Take any point O inside the polygon. Join OA, OB, O..

If a straight line meets another straight line, the adjacent angles so formed are supplementary. A straight line CO meets straight line AB at O. ..