Note: Your teacher will grade your response to ensure you receive proper credit for your answers. Given , explain how to construct a square with sides of length AB.
To construct a square with sides of length AB, follow these steps:
1. Draw a straight line segment AB of the given length. This will serve as one side of the square.
2. From point A, use a compass to mark a point C on the same line segment AB, but this time, the distance between A and C should be equal to the length of AB.
3. Using the compass, place its needle on point C and set its width to match point A. Then, draw an arc above line segment AC.
4. Without changing the compass width, place its needle on point A and draw another arc that intersects the arc drawn in the previous step, resulting in a point D.
5. Connect points C and D with a straight line. This line segment should be perpendicular to AB.
6. Now, using the compass, place its needle on point D and set its width to match point A. Then, draw an arc that intersects line segment CD.
7. Without changing the compass width, place its needle on point C and draw another arc that intersects the arc drawn in the previous step, resulting in a point E.
8. Connect points D and E with a straight line. This line segment will be parallel to AB and should be the same length as AB, creating two equal adjacent sides.
9. Finally, complete the square by connecting points E and B with a straight line segment, resulting in a square with sides of length AB.
Ensure that the angles created by the construction are right angles to have a perfect square.