Unit 1, Lesson 7
Construction Techniques 5: Squares
Geometry
Practice
Problem 2
This diagram is a straightedge and compass construction of a square \(BACD\) (not all markings are shown). The construction followed these steps:
Diagram of construction of square B A C D. Two sets of parallel lines intersect to create a square. Point A is on bottom left, Point B bottom right, Point C top right, Point D top left. A circle is drawn through the inside of the square, intersecting points B and C.
- Start with two marked points \(A\) and \(B\).
- Use a straightedge to construct line \(AB\).
- Use a previous construction to construct a line perpendicular to \(AB\) passing through \(A\).
- Use a previous construction to construct a line perpendicular to \(AB\) passing through \(B\).
- Use a compass to construct a circle centered at \(A\) passing through \(B\).
- Label an intersection point of that circle and the line from the third step as \(C\).
- Use a previous construction to construct a line parallel to \(AB\) passing through \(C\).
- Label the intersection of that line and the line from the fourth step as \(D\).
- Use a straightedge to construct the segments \(AC\), \(CD\), and \(DB\).
Explain why you need to construct a circle in the fifth step.