Name _________________________
3/19/15
1. Hide the axes. This can be done by right clicking, and then clicking on “axes.”
2. Construct a triangle by selecting “polygon” on the top banner. Then, plot three vertices,
and click on the first vertex a second time in order to complete the process.
It should look something like this. I recommend starting with an acute triangle.
3. Select “circle with center through point” on the top banner, and construct a circle with
its center at vertex A. Click once on point A, and once inside triangle ABC.
4. Continuing to use the circle tool, construct two additional circles using the two
intersections created by the first circle. Click on the first intersection (to make it the
center) and the second intersection (to place a point on the circle). Then, repeat the
process, but switch the intersection that is on the circle and the intersection that is the
center.
It should look something like this.
And then like this.
5. On the top banner, click on “line.” Then, on the drop down, click “ray.”
6. Start the ray on vertex A, and place the second point of the ray at the intersection of
your second and third circles.
Name _________________________
3/19/15
7. Hide all of the conics and points (except for the three vertices). This can be done by
clicking on the circles on the left side of the page.
8. Repeat steps 3-7, but this time start at vertex B.
9. Repeat steps 3-7, but this time start at vertex C.
This point of concurrency is known as the icenter.
Did we know where that ray was going to be before we constructed the angle bisector of
vertex C?
10. Plot a point on the point of concurrency. Click on “point” on the top banner, and select
the spot where all three lines intersect.
11. Change the color of the point to red. Right click on the point. Select “properties” at the
bottom. Select the color tab, and then select red.
Name _________________________
3/19/15
Right now you have an acute triangle. Where is the point of concurrency located?
Change your triangle to an obtuse triangle (by moving one or more of the vertices). Where is
the point of concurrency located now?
Change your triangle so that it closely resembles a right triangle. Where is the point of
concurrency?
What hypothesis can we make about the incenter?
Construct a perpendicular line through segment ab that goes through your incenter (Look
below question if you need the directions for this). Why do you think I am constructing a
perpendicular?
Steps to constructing a perpendicular.
1. Select “perpendicular line” on the top banner of the screen. Then click on your incenter
and segment ab.
Construct a circle with the center at your incenter and a point on the circle being the point of
intersection that the perpendicular makes with line segment AB. Refer back to step three if you
forgot how to construct a circle.
What do you notice? Try moving your vertices. Does anything change?
Name _________________________
3/19/15
1. Construct another acute triangle.
2. Construct the three perpendicular bisectors.
*This can be done by going through the steps in the construction. I will give the shortcut
steps*
3. Select “point” on the top banner. On the drop down, select “midpoint or center” (5th
item down).
4. Click on segments AB, BC, and CD. This should create three midpoints.
5. Select “perpendicular line” on the top banner. Select the midpoint first, and then the
segment the point is on. Do this for all three segments.
This point of concurrency is called the circumcenter.
Right now you have an acute triangle. Where is the point of concurrency located?
Change your triangle to an obtuse triangle (by moving one or more of the vertices). Where is
the point of concurrency located now?
Change your triangle so that it closely resembles a right triangle. Where is the point of
concurrency?
What can we conclude about the circumcenter if we made it the center of a circle?