In the given figure, AL || DC, E is mid point of BC. Show that `DeltaEBL ~= DeltaECD`.

In the given figure, AB||DC and AD||BC show that DeltaABC ~= Delta CDA .

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.

In the given figure AB || CD, BC || DE then find the values of x and y

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

In the given figure, AD is perpendicular to BC and EF || BC, if /_ EAB = /_ FAC , show that triangles ABD and ACD are congruent. Also, find the values of x and y if AB = 2x + 3, AC = 3y + 1, BD = x and DC = y + 1.

In the given figure, AB || CD || EF. given that AB=7.5 cm, DC= y cm EF = 4.5 cm and BC = x cm, find the values of x and y.

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

DeltaABC and DeltaBDE are two equilateral triangles. If D is the mid-point of BC , then the ratio of the areas of DeltaABC and DeltaBDE is