In the adjacent figure, we have `BX = 1/2 AB, BY = 1/2 BC` and AB=BC. Show that BX = BY.

In the adjacent figure, AC = AE, AB = AD and /_ BAD = /_ EAC . Show that BC = DE.

In the adjacent figure, AB = BC and AC = CD . Prove that : /_ BAD : /_ ADB = 3 : 1.

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 adjacent figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC||PR. Show that BC || QR.

In the adjacent figure DeltaABC, D is the midpoint of BC. DE_|_AB, DF_|_AC and DE = DF . Show that DeltaBED ~= Delta CFD .

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 .

In the adjoining figure if DE||BC , then (AB)/(BD)=(AC)/(CE) .

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 figure given below, show that length AH gt AB + BC + CD .