l and m are two parallel lines intersected by another pair of parallel lines p and q . Show that `DeltaABC~= DeltaCDA`.

l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that triangleABC ~= triangleCDA

l, m and n are three parallel lines intersected by the transversals p and q at A, B, C and D,E, F such that they make equal intercepts AB and BC on the transversal p. Show that the intercepts DE and EF on q are also equal.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel line intersecting another set of three parallel lines is:

m parallel lines in a plane are intersected by a family of n parallel lines. The total number of parallelograms so formed is :

Does Euclid's fifth postulate imply the existence of parallel lines? Explain .

Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD. Show that (i) DeltaAOB ~= DeltaDOC (ii) O is also the mid-point of BC.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed . Show that ar (ABCD) = ar (PBQR)

ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6. If A lies between the parallel lines at a distance 4 from one of them, then the length of a side of the equilateral triangle is :

A line intersecting a circle in two points is called a secant .

The distance between the pair of parallel lines x^(2)+4 x y+4 y^(2)+3 x+6 y-4=0 is