Given: AD = BC and AD || BC Prove: ABCD is a parallelogram.
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The steps to construct a parallelogram using a ruler and a compass are;
1. Draw a starting line segment <em>l</em> linger than 8 cm.
2. Mark point <em>K</em> on the line segment.
3. Widen the compass to a radius of 8 cm using the ruler.
4. Place the compass at point <em>K</em> and with the 8 cm radius mark point <em>L</em> on the line <em>l</em>.
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5. At point <em>L</em> construct a 45° angle as follows;
- Draw arcs that intersect line <em>l</em> on both sides of point <em>L.</em>
- From each of the intersection points, draw arcs that intersect each other on on the upper area adjacent to line <em>l</em><em>.</em>
- From the intersection point in the previous step, draw a line to point <em>L</em> to get a perpendicular line to line <em>l</em>.
- Draw arcs to intersect the perpendicular line and line <em>l</em> on the other side of point <em>L</em> from <em>K</em>.
- From the points the arc intersects the perpendicular line draw arcs of the same radius to intersect at a point <em>X</em> to the right of the perpendicular line.
The above steps bisects the 90° angle of the perpendicular lines.
- Join point <em>X</em> to point <em>L </em>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 <em>L</em> draw an arc to intersect XL at <em>M</em>.
7. At point <em>M</em> construct a line YM at 45° angle to the line <em>l</em>.
8. From point <em>M</em> draw an arc to intersect YM and label the point as point <em>N</em>.
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:
brainly.com/question/1528158?section=similar
Answer:
40 >_m
Step-by-step explanation:
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