Question

this diagram is a straightedge and compass construction of a square bacd (not all markings are shown). the construction followed these steps: 1. start with two marked points a and b. 2. use a straightedge to construct line ab. 3. use a previous construction to construct a line perpendicular to ab passing through a. 4. use a previous construction to construct a line perpendicular to ab passing through b. 5. use a compass to construct a circle centered at a passing through b. 6. label an intersection point of that circle and the line from step 3 as c. 7. use a previous construction to construct a parallel to ab passing through c. 8. label the intersection of that line and the line from step 4 as d. 9. use a straightedge to construct the segments ac, cd, and db. explain why you need to construct two perpendicular lines through ab in steps 3 and 4.

Explanation:

A square has four right - angled corners. Constructing two perpendicular lines to \(AB\) through \(A\) and \(B\) gives two of the right - angled corners of the square and also helps in defining the parallel sides of the square.

Answer:

To create right - angled corners and parallel sides for the square.