PQRS is a parallelogram. K. L are the midpoints on PQ, RS respectively. `bar(PL)` intersects `bar(SK)` at M and RK and QL intersects at N. Show that KNLM is a parallelogram.

ABCD is a parallelogram and P, Q are the mid points of bar(AD) and bar(BC) respectively. Show that : bar(BD) and bar(PQ) bisect each other.

ABCD is a parallelogram and P, Q are the mid points of bar(AD) and bar(BC) respectively such that AP=1/3AD and CQ=1/3BC,Show that : AQCP is a parallelogram.

In a parallelogram PQRS, M and N are the points on bar(PQ) and bar(RS) such that PM=RN. prove that MS is parllel to NQ

Fill in the Blanks:In a parallelogram PQRS, the bisectors of consecutive angles P and Q intersect at K. angle PKQ =____.

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.

Assertion (A) : If 5 parallel lines intersect 4 parallel lines, then the number of parallelograms formed is 80 Reason (R) : The number of parallelograms formed when a set of m parallel lines are intersecting another set of n parallel lines is ""^(m)C_(2)xx""^(n)C_(2) The correct answer is

If a set of 'm' parallel lines intersect another set of 'n' parallel lines (not parallel to the lines in the first set), then find the number of parallelograms formed in this lattice structure.