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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