construct parallelogram ABCD given AC=4.2cm, AB=4.6cm, BD=5.8cm. Measure the side bc

Question

AC+4.2, AB=4.6cm, BD=5.8cm. measure the side bc

Answer 1

To solve this problem, use the fact that 2 diagonals of a parallelogram bisect each other.

Mark point A, and from A, draw a horizontal ray rightwards. Mark point B on the ray exactly 4.6cm away from A.  Draw 2 arcs above AB: one from A with radius 2.1cm (=½·AC), and the other from B with radius 2.9cm (=½·BD), and mark the crossing of 2 arcs O.

Extend AO and BO upwards.  From O, draw 2 arcs: one with radius OA (=½·AC) crossing the extension of AO at C, and the other with radius OB (=½·BD) crossing the extension of BO at D.  Connect B to C, C to D and D to A.

Check if AB=CD and BC=DA.  CKD.  Therefore quadrilateral ABCD is the required parallelogram, and BC=approx. 2.12cm