Using a ruler and a pair of compasses ONLY,construct: A trapezium ABCD such that /AB/=7.5CM,<ABC=120',BC//AD,/AD/=10.5cm,and /AC/=9.5cm.
To construct the trapezium ABCD using only a ruler and a pair of compasses, follow these steps:
1. Draw a line segment AB using your ruler and make it 7.5 cm long.
2. Place the compass at point A and draw an arc with a radius of 9.5 cm to intersect line AB. Let the point of intersection be C.
3. With the same compass width, place the compass at point B and draw an arc to intersect line AB. Let the point of intersection be D.
4. Draw lines AC and BD to complete the trapezium.
5. Measure the angle ABC using a protractor and find that it is 120 degrees. Since the ruler and compass can't measure angles directly, you can use the constructed 120-degree angle as a reference for other angles if needed.
6. Measure the length of AD using your ruler and find it to be 10.5 cm.
Now you have successfully constructed a trapezium ABCD with the given specifications using only a ruler and a pair of compasses.