Given Modifying above Upper A Upper B with bar, explain how to construct a square with sides of length AB.
To construct a square with sides of length AB, we can use the method of "bar and parallel lines":
1. Begin by drawing a line segment AB of the desired length.
2. Place the midpoint of segment AB, and mark it as point M.
3. Draw a line passing through point M that is perpendicular to segment AB. This line will intersect AB at M.
4. Using a compass, place the needle at point M and open it to a distance that reaches beyond point A and point B. This distance should be equal to the length of AB.
5. Keeping the compass open at this distance, place the compass needle at point A and draw an arc that intersects the perpendicular line at point P.
6. Without changing the compass width, place the compass needle at point B and draw another arc intersecting the perpendicular line at point Q.
7. Draw the line segment PQ. This line segment will be parallel to AB and of equal length.
8. Now, with AB as the base and PQ as the height, we have a rectangle. To construct a square, we need to make one more side equal to AB.
9. Using a compass, measure the length of AB and place it at point Q. Draw an arc from point Q that intersects line segment PQ at point R.
10. Connect point R to point A. This line segment AR will be equal in length to AB.
11. Finally, draw the line segments BR and AR to complete the square ABCD, where AB is the desired side length.
This construction guarantees that all four sides of the square will be equal in length to AB.
To construct a square with sides of length AB, follow these step-by-step instructions:
1. Start by drawing a line segment representing AB with points A and B.
2. Since we are asked to modify upper A upper B with a bar, draw a straight line segment perpendicular to AB passing through the midpoint of segment AB. This line will intersect AB at a point, let's call it C.
3. Now draw another line segment perpendicular to AB passing through point C. This line will intersect AB at another point, let's call it D.
4. Use a compass to set the width of segment CD. Place the compass tip at point C and draw an arc that intersects the line you drew in step 2.
5. Without changing the compass width, place the compass tip at point D and draw another arc that intersects the same line. The two arcs should intersect each other.
6. Connect the intersection points of the arcs with a straight line. This line segment will represent one side of the square.
7. Now, using the compass, measure the length of segment CD. Place the compass tip at point A and draw an arc that intersects AB.
8. Without changing the compass width, place the compass tip at point B and draw another arc that intersects AB. The two arcs should intersect each other.
9. Connect the intersection points of the arcs with a straight line. This line segment will be another side of the square and should be perpendicular to the first side drawn.
10. Repeat steps 7 to 9 for the other two sides of the square, using points C and D to measure the length of the remaining sides.
11. Finally, connect the four sides of the square to complete the construction.
You have successfully constructed a square with sides of length AB.