Download Incenter (and Inscribed Circle)

Creating the Centers of Triangles Worksheet
Go to this website:
https://app.geogebra.org/#geometry
Circumcenter (and Circumcircle):
1. Click on the triangle symbol and select Polygon.
2. Click to create the first vertex.
3. Move the cursor and click again to create the second vertex.
4. Move the cursor again and click to create the third vertex.
5. Move the cursor back onto the first vertex and click to create the triangle.
6. Click on the symbol with a segment intersected by a line and select Perpendicular Bisector.
7. Click on each of the sides of the triangle to create their perpendicular bisectors.
8. All three lines should intersect in the same point. Click on the button with a point and A and
then select Point.
9. Click on the intersection of the perpendicular bisectors. This is the circumcenter.
10. Click on the button with a circle on it and select Circle with Center through Point.
11. Click on the circumcenter.
12. Move the cursor so that it is over one of the vertices of the triangle and click. The circle created
is called the circumscribed circle, or the circumcircle.
13. Click on the cursor button and select move. Change your triangle by moving the vertices. What
happens as you do this? Write down some patterns you notice as you move the triangle.
14. Take a screenshot and upload the picture to google classroom.
Incenter (and Inscribed Circle):
1. Create a triangle using the polygon button.
2. Go to the construction button (where the perpendicular bisector button was) and click on angle
bisector.
3. Then click on each of the three vertices in order to create an angle bisector from the middle
vertex.
4. Do step three two more times. Make sure that a different vertex is clicked second each time.
5. Click on the point button. Then click on the intersection of the angle bisectors. This is the
incenter.
6. Click on the button for the angle bisectors, but select perpendicular line.
7. Select the incenter and then click on one of the sides of the triangle. This will create a
perpendicular line that shows the radius of the inscribed circle.
8. Select the point button. Click on the point where the perpendicular line you created intersects
the side of the triangle.
9. Select the Circle with Center through Point button. Create a circle with the incenter as the
center and the point on the side of the triangle as the other point.
10. The circle you just created is called the inscribed circle.
11. Click on the cursor and select the move button. Move the triangle by clicking and dragging the
vertices. Write down any patterns you see.
12. Take a screenshot and upload it to google classroom.
Medians and the Centroid
1. Create a triangle.
2. Click on the point button and select Midpoint or Center.
3. Click on each side of the triangle to find the midpoint.
4. Click on the line button and select segment.
5. Create a segment from one of the vertices to the midpoint of the side opposite that angle.
6. Repeat step 5 for the other two vertices. These segments are called medians.
7. Click on the point button and select point. Click on the intersection of the medians. This point is
called the centroid.
8. Click on the cursor button and select move. Move the triangle by dragging the sides and
vertices. Write down any patterns you see.
9. Take a screenshot and upload it to google classroom.
Altitudes and the Orthocenter
1. Create a triangle.
2. Click on the construction button and select perpendicular line.
3. Click on one vertex of the triangle and then select the opposite side. This is called the altitude of
a triangle.
4. Create the other two altitudes.
5. Click on the point button and select Point. Then click on the intersection of the altitudes. This is
called the Orthocenter.
6. Click on the cursor and select the move button. Move the triangle around and write down any
patterns you see.