Question

answer the whole of this question on a sheet of plain paper. use ruler and compasses only for all constructions and show clearly all construction lines and arcs. all constructions should be done on a single diagram. (a) construct a quadrilateral abcd in which ab = 8.5 cm, ad = 7 cm, dc = 5 cm, ∠adc = 90° and ∠bad = 60°. 6

Explanation:

Step1: Draw side AD

Draw a line segment AD of length 7 cm using a ruler.

Step2: Construct angle BAD

Using a compass, at point A, construct an angle ∠BAD = 60°. With A as the center, draw an arc of any radius. Let it intersect the arms of the angle at two - points. Then, from these two intersection points, draw arcs of equal radius inside the angle. The point of intersection of these two arcs gives the angle - bisector of the constructed 60° angle. Mark a point B on the arm of the 60° angle such that AB = 8.5 cm.

Step3: Construct angle ADC

At point D, using a compass, construct a right - angle ∠ADC = 90°. With D as the center, draw an arc of any radius. Let it intersect the arm of the angle at two points. Then, from these two intersection points, draw arcs of equal radius inside the angle. The point of intersection of these two arcs gives the angle - bisector of the constructed 90° angle.

Step4: Locate point C

With D as the center and a radius of 5 cm, draw an arc to intersect the arm of the 90° angle at point C.

Answer:

A quadrilateral ABCD is constructed as per the given requirements.