Question

1. 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 line parallel to ab passing through c 8. label the intersection of that line and the line from step 4 as d

Explanation:

Step1: Recall properties of a square

A square has four equal - length sides and four right - angles. The construction starts by creating a base line \(AB\).

Step2: Perpendicular lines creation

Steps 3 and 4 create two lines perpendicular to \(AB\) at points \(A\) and \(B\) respectively. This gives us two right - angles at \(A\) and \(B\).

Step3: Circle construction

In step 5, a circle centered at \(A\) passing through \(B\) is constructed. The radius of the circle \(r = AB\). When we find the intersection point \(C\) (step 6), \(AC=AB\) since \(C\) lies on the circle centered at \(A\) with radius \(AB\).

Step4: Parallel line construction

Step 7 constructs a line parallel to \(AB\) through \(C\). When this line intersects the perpendicular line at \(B\) (step 8), we get the fourth vertex \(D\). Since \(AC = AB\) and the angles are right - angles, and the opposite sides are parallel, \(BACD\) is a square.

Answer:

The steps described correctly construct a square \(BACD\) because they ensure that all four sides are of equal length and all four angles are right - angles.