1. Is it possible to construct a triangle that has sides of length 5 cm, 2 cm, and 9 cm? If yes, explain how to construct one. If not, explain why it is impossible.

2. Say what these terms mean in geometry:

a) Point

b) Segment

c) Line

d) Ray

e) Circle

3. Explain the difference between a constructed geometric figure and a drawn geometric figure?

4. Given points A and B (below):

a) Construct two points (label them H and J) that are equidistant from points A and B (below). Explain how you can be sure that the points you’ve constructed are equidistant from A and B.

Construction:

Explanation:

b) Construct segment HJ. What do you suspect is true about all the points on segment HJ?

5. Given points E and F (below), explain a strategy for constructing a point X so that X is 3 times as far from F as it is from E. Then, construct point X. Explain how you know that the point you have constructed really has is 3 times as far from F as it is from E.

Strategy:

Construction:

Explanation:

6. Ben, Juan, and Suzy lived on three different ranches in a sparsely settled area of the Mojave desert. They wanted to form an Elvis fan club, but they needed to settle on a meeting place. Now, each of the three is highly self-centered and wants to have the club headquarters at his or her house. But none of the three want to be any farther from club headquarters than anybody else. They agreed that they would set up a tent at a spot equidistant from all three of their homes. They got out a map, but each time they picked a spot someone would insist that they had been slighted by having to travel farther than someone else.

Give a strategy for locating a place on the map so that it is the same distance from each of Ben’s, Juan’s, and Suzy’s house. Then construct a point Y that represents that point. Finally, explain how you know that your construction locates a point on the map that everyone should be happy with.

Strategy:

Construction:

Explanation: