# Lesson 1

Build It

### Problem 1

Here is a diagram of a straightedge and compass construction. $$C$$ is the center of one circle, and $$B$$ is the center of the other. Explain why the length of segment $$BD$$ is the same as the length of segment $$AB$$.

### Problem 2

Clare used a compass to make a circle with radius the same length as segment $$AB$$. She labeled the center $$C$$. Which statement is true?

A:

$$AB > CD$$

B:

$$AB = CD$$

C:

$$AB > CE$$

D:

$$AB = CE$$

### Problem 3

The diagram was constructed with straightedge and compass tools. Points $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ are all on line segment $$CD$$. Name a line segment that is half the length of $$CD$$. Explain how you know.

### Solution

This diagram was constructed with straightedge and compass tools. $$A$$ is the center of one circle, and $$C$$ is the center of the other.
1. The 2 circles intersect at point $$B$$.  Label the other intersection point $$E$$.
2. How does the length of segment $$CE$$ compare to the length of segment $$AD$$?