Construct each of the following and give justification:

A rhombus whose diagonals are 4 cm and 6 cm in lengths.

Steps of Construction:

(i) Draw ray XY.

(ii) Draw perpendicular bisector of XY.

(iii) Let the intersection point be O.

(iv)With O as centre, and radius 2 cm (since 4/2 = 2), cut arcs on XY as C and D.

Similarly with O as centre, and radius 3 cm(since 3 + 3 = 6), cut arcs on both sides of the bisector as AB.

(v)Join AC, AD, BC and BD.

Thus, ABCD is the required rhombus.