Question

Using ruler and compasses only, construct a parallelogram KLMN, so that KL = 8 cm, LM = 6 cm and angle KLM = 135°.​

Answer 1

The steps to construct a parallelogram using a ruler and a compass are;

1. Draw a starting line segment l linger than 8 cm.

2. Mark point K on the line segment.

3. Widen the compass to a radius of 8 cm using the ruler.

4. Place the compass at point K and with the 8 cm radius mark point L on the line l.

5. At point L construct a 45° angle as follows;

• Draw arcs that intersect line l on both sides of point L.

• From each of the intersection points, draw arcs that intersect each other on on the upper area adjacent to line l.

• From the intersection point in the previous step, draw a line to point L to get a perpendicular line to line l.

• Draw arcs to intersect the perpendicular line and line l on the other side of point L from K.

• From the points the arc intersects the perpendicular line draw arcs of the same radius to intersect at a point X to the right of the perpendicular line.

The above steps bisects the 90° angle of the perpendicular lines.

• Join point X to point L with a straight line to form ∠XLM = 135° (90° + 45° = 135°)

6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.

7. At point M construct a line YM at 45° angle to the line l.

8. From point M draw an arc to intersect YM and label the point as point N.

9. Join point M and N to complete the construction of the parallelogram KLMN.

Learn more about construction using a compass and a ruler here:

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