# 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 \(AB\).

### Solution

For access, consult one of our IM Certified Partners.

### 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?

\(AB > CD\)

\(AB = CD\)

\(AB > CE\)

\(AB = CE\)

### Solution

For access, consult one of our IM Certified Partners.

### 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

For access, consult one of our IM Certified Partners.

### Problem 4

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

- The 2 circles intersect at point \(B\). Label the other intersection point \(E\).
- How does the length of segment \(CE\) compare to the length of segment \(AD\)?

### Solution

For access, consult one of our IM Certified Partners.