# Lesson 3

Construction Techniques 1: Perpendicular Bisectors

- Let’s explore equal distances.

### Problem 1

This diagram is a straightedge and compass construction. \(A\) is the center of one circle, and \(B\) is the center of the other. Select **all** the true statements.

Line \(CD\) is perpendicular to segment \(AB\)

Point \(M\) is the midpoint of segment \(AB\)

The length \(AB\) is the equal to the length \(CD\).

Segment \(AM\) is perpendicular to segment \(BM\)

\(CB+BD > CD\)

### Problem 2

In this diagram, line segment \(CD\) is the perpendicular bisector of line segment \(AB\). Assume the conjecture that the set of points equidistant from \(A\) and \(B\) is the perpendicular bisector of \(AB\) is true. Is point \(E\) closer to point \(A\), closer to point \(B\), or the same distance between the points? Explain how you know.

### Problem 3

Starting with 2 marked points, \(A\) and \(B\), precisely describe the straightedge and compass moves required to construct the triangle \(ABC\) in this diagram.

### Problem 4

This diagram was created by starting with points \(C\) and \(D\) and using only straightedge and compass to construct the rest. All steps of the construction are visible. Select **all** the steps needed to produce this diagram.

Construct a circle centered at \(A\).

Construct a circle centered at \(C\).

Construct a circle centered at \(D\).

Label the intersection points of the circles \(A\) and \(B\).

Draw the line through points \(C\) and \(D\).

Draw the line through points \(A\) and \(B\).

### Problem 5

This diagram was constructed with straightedge and compass tools. \(A\) is the center of one circle, and \(C\) is the center of the other. Select **all** true statements.

\(AB=BC\)

\(AB=BD\)

\(AD=2AC\)

\(BC=CD\)

\(BD=CD\)