In the given Fig, M is the mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL = 2 BL. 

In the given Fig., ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE, and hence find the lengths of AE and DE.

In the given fig., DE || BC and AD : DB = 5:4. Find .

In the given Fig., PQ || BC and AP: PB = 1:2. Find

In the given Fig,  if the area of XYZ is 32 cm², then find the area of the quadrilateral PYZQ.

320. Prove that in any triangle, the sum of the squares of any two sides is equal to twice the square of half of third side together with twice the square of the median which bisects the third side.