Question

Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, <B = 60°, AD = 5 cm and D is equidistant from AB and BC. Measure CD.

Answer 1

1. Draw line segment AB = 6 cm.
2. At point B, construct angle ∠B = 60°.
3. On the ray of the angle at B, mark point C such that BC = 5 cm.
4. Join AC to form triangle ABC.
5. Since point D is equidistant from AB and BC, point D lies on the bisector of ∠B.
6. Draw the bisector of ∠B; this is the locus of points equidistant from AB and BC.
7. From point A, draw an arc of radius 5 cm (AD = 5 cm); it intersects the bisector of ∠B at point D.
8. Join CD.
9. Measure the length of the CD using a ruler.