See2Learn Gaṇita

The Fact: Square of a leg of a right angled triangle is equal to the product of the hypotenuse and the projection of that leg on the hypotenuse. Visual Proof: For the longer leg. The point B is moveable.      For the shorter leg The point B is moveable. 

The fact: The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hypotenuse is split into. OR In a right angled triangle, the square of the altitude drawn to the hypotenuse from the right angle is equal to the product of the projections of the legs on the hypotenuse.  The Visual proof:

 Generating rational right-angled triangles.

 Here is an idea to divide a line segment into equal parts. The lines printed on a ruled sheet of paper are used to divide a line segment into equal parts. Application The above idea of using equidistant parallel lines for dividing a line segment is used to divide a rope into 7 equal parts which in turn is wrapped around a circular object to divide the circumference of that circular object into 7 equal parts.