GEOMETER'S SKETCHPAD
ASSIGNMENT #6 (Youngberg)
Note the following instructions as you complete this assignment and all other GSP assignments:
•
•
•
Although you will be emailing your assignment to me, save a copy of all of your sketches to your disk.
Answer all of the questions posed to you in a text box at the bottom of the sketch you are currently working
on.
Make sure that all of your sketches are constructions, not drawings. That is, create all sketches so that the
required geometric relationships are maintained when any object is “dragged.”
1. To demonstrate that GSP can be used as an electronic compass and straightedge, complete this problem without
using the Construct menu. That is, use only the point tool to construct points, the straightedge tool to construct
lines/segments/rays, and the compass tool to construct circles. There is one exception—you may use the
Construct menu to construct a circle by its center and radius. So, the only construction menu item that you are
allowed to use in this problem is Circle By Center+Radius. (After completing this problem, feel free to use the
Construct menu as usual.)
a) In a new sketch, draw an arbitrary segment AB . Construct the midpoint of AB and the perpendicular
bisector of AB . Label the midpoint M. (Hint: follow Construction 6 that we learned in class). Do not
hide the objects that you used in your construction. Save your sketch as GSP 6A (perpendicular bisector).
b) In a new sketch, draw an arbitrary line, l, and a point, P, which is not on the line. Construct a line
perpendicular to l that passes through P. (Hint: follow Construction 4 that we learned in class). Save your
sketch as GSP 6B (perpendicular line).
c) In a new sketch, construct a regular octagon. Use the idea on page 838 of your text to construct the
octagon. Hide everything that you use in your construction except for the circle, the perpendicular lines and
the angle bisectors. Construct the hexagon from thick lines so that it stands out. Your final sketch should
look something like the drawing below. Save your sketch as GSP 6C (regular octagon).
2. Draw an arbitrary triangle ABC. Construct the circumcenter and the circumcircle of the triangle. Label the
circumcenter O. (Hint: See pages 835-836 of your text to see how to construct the circumcenter and
circumcircle.) Hide everything except for triangle ABC, its circumcenter and its circumcircle. Color in the
circumcircle and the triangle (by constructing their interiors) so that your sketch looks something like the figure
below.
B
O
A
C
Drag the points A, B, and C to change the triangle, and notice that the circumcenter lies inside the triangle for
some triangles and outside the triangle for others.
QUESTION 1: What kind of triangle is ∆ABC when the circumcenter lies inside the triangle?
QUESTION 2: What kind of triangle is ∆ABC when the circumcenter lies outside the triangle?
QUESTION 3: What kind of triangle is ∆ABC when the circumcenter lies on the triangle?
Save your sketch as GSP 6D (circumcircle).
3. Draw an arbitrary triangle ABC. Construct the incenter and the incircle of the triangle. Label the incenter I.
(Hint: See pages 837-838 of your text to see how to construct the incenter and incircle.) Hide everything except
for triangle ABC, its incircle and its incenter. Color in the incircle and the triangle (by constructing their
interiors) so that your sketch looks something like the figure below. Save your sketch as GSP 6E (incircle).
B
A
C