# Lesson 3

Construction Techniques 1: Perpendicular Bisectors

### 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.

A:

Line $CD$ is perpendicular to segment $AB$

B:

Point $M$ is the midpoint of segment $AB$

C:

The length $AB$ is the equal to the length $CD$.

D:

Segment $AM$ is perpendicular to segment $BM$

E:

$CB+BD > CD$

### 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.

### Solution

(From Unit 1, Lesson 2.)

### 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.

A:

Construct a circle centered at $A$.

B:

Construct a circle centered at $C$.

C:

Construct a circle centered at $D$.

D:

Label the intersection points of the circles $A$ and $B$.

E:

Draw the line through points $C$ and $D$.

F:

Draw the line through points $A$ and $B$.

### Solution

(From Unit 1, Lesson 2.)

### 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.

A:

$AB=BC$

B:

$AB=BD$

C:

$AD=2AC$

D:

$BC=CD$

E:

$BD=CD$