State and prove Basic proportionality theorem

State "Basic proportionality theorem"

Study the following figure. Write the ratios in relation to basic proportionality theorem and its corollarise, in terms of a, b, c and d.

State and prove Bionomial theorem for any positive integer n.

If the diagonals of a quadrilateral divide each other proportionally, then prove that the quadrilateral is a trapezium.

State and explain parallel axis theorem and perpendicular axis theorem.

State and prove conservation of linear momentum in case of collision of two bodies.