Question

Without using set square or protractor, construct the parallelogram ABCD in which AB = 5.1 cm, the diagonals AC = 5.6 cm and the diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BС.

Answer 1

• Draw a line segment AB = 5.1 cm.
• Find the midpoint O of AC and BD (since diagonals of a parallelogram bisect each other).
  Take AO = OC = 2.8 cm along one line, and BO = OD = 3.5 cm along another line through O to locate C and D.
• Join A to C, B to C, A to D, and B to D to get parallelogram ABCD.
• At B, construct the angle bisector of ∠ABC and extend it to meet side DC at P.

In a parallelogram, diagonals bisect each other, so taking half of AC and BD from their intersection gives the correct positions of C and D. A point that is equidistant from the lines AB and BC lies on the angle bisector of ∠ABC. Therefore, the intersection point P of side DC with the angle bisector of ∠ABC is equidistant from AB and BC.