Construct the following and give justification :

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

Answers (1)

Given : Rhombus with diagonals length = 4 cm, 6 cm

Steps of Construction :

            1.         Draw a line AB = 4 cm

            2.         Bisect the AB using another line EF which intersects it at point X  

                        E X F is perpendicular to AB

            3.         As center X mark an arc of 3 cm as the radius on XF and XE which intersects at C and D respectively.

            4.         Join AD, AE, BC, BD

            ACBD is the required rhombus.

            Justification :

         DC\perp AB hence  DA = DB, AC = BC   …..(1) 

            {every point on perpendicular bisector of line is equidistance from end points of line}

                       \angle DXB=90^{\circ}

            Also,    XD = XC = 3 cm

            Thus,   AB is perpendicular to DC

                        BD = BC         …..(2)

            From 1 and 2, ABCD is a rhombus.

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