alternate segment theorem

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

Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the..

If a transversal intersects two parallel lines, then each pair of alternate angles are equa..

The locus of a point equidistant from two fixed points is the perpendicular bisector of the segment joining the two point..

Statement - The locus of a point equidistant from two fixed points is the perpendicular bisector of the segment joining the two points. This theorem is proved in two parts. First prove that any point on the locus satisfies the conditio..

Statement - If a transversal intersects two parallel lines, then each pair of alternate angles are equa..

Theorem 1 - 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..

Gauss' Theorem - We have already learnt to find the electric field intensity due to a charged conductor using Coulomb's law. Gauss' theorem can also be used to calculate the electric field intensity provided there is a symmetry in the charge distribution. Can be considered as an..

If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are paralle..

Introduction - We can prove some more properties of triangles using the properties of parallelograms seen in the previous chapter. We find that the line segment joining the mid points of any two sides of the triangle is parallel to the third side and is equal to half of it. We prove this ..