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 youÕve 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 BenÕs, JuanÕs,
and SuzyÕs 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: