Question

1. this diagram is a straightedge and compass construction of a square bacd (not all markings are shown). the construction followed these steps: a. start with two marked points a and b b. use a straightedge to construct line ab c. use a previous construction to construct a line perpendicular to ab passing through a d. use a previous construction to construct a line perpendicular to ab passing through b e. use a compass to construct a circle centered at a passing through b f. label an intersection point of that circle and the line from step 3 as c g. use a previous construction to construct a line parallel to ab passing through c h. label the intersection of that line and the line from step 4 as d i. use a straightedge to construct the segments ac, cd, and db explain why you need to construct a circle in step 5.

Explanation:

In a square, all sides are equal. By constructing a circle centered at A passing through B, we ensure that the distance from A to C (a radius of the circle) is equal to the distance from A to B. This helps in creating a side - length for the square equal to the given line segment AB, as we need to have equal - length sides to form a square.

Answer:

To ensure that the side AC of the square has the same length as side AB. Since in a square all sides are equal, and the radius of the circle centered at A passing through B (which is AC) will be equal to AB, helping to construct a square with equal - length sides.