theorem 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..

What postulates / theorems are needed to prove the congruency of ΔABC &ΔPQR? 1. Base Angle theorem 2. SSS Postulate 3. SAS Postulate => 1 only or 1 & 3 only or 1 & 2 only or 3 only..

Theorem 2 (Converse of Theorem 1) - If two angles of a triangle are equal, the sides opposite to these angles are equal. In AB = AC Draw AD, the bisector of to meet BC at ..

If three concurrent forces acting on a body keep it in equilibrium, then each force is proportional to the sine of angle between the other two forces. Þ If three concurrent forces keep a body A in equilibrium, the 3 forces must be coplanar..

The area of a parallelogram is equal to that of a rectangle of the same base and of the same altitude. ABCD is a parallelogram and ABEF is a rectangle. They have common base AB and same height AF (or BE) Corollary Parallelograms having equal bases and equal altitudes are equal in area. A diagonal b..

If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equa..

If two statements are such that the hypothesis of one is the conclusion of the other and vice-versa then either of the statement is said to be the converse of the other..

This theorem is a consequence of the principle of conservation of energy, applied to ideal liquids in motion. The theorem states that: For the streamline flow of an ideal liquid, the total energy (sum of pressure energy, potential energy and kinetic energy) per unit mass remains..