Perpendicular Bisectors of a Triangle
Lab (gsp)
Construct
DEF
1. Open a new sketch in sketchpad.
2. Using the segment tool, create DEF. Highlight the points in order then using
the drop-down menu go to Display – Show Labels. A pop-up menu will appear
with Label, make sure type “D” in the box then click Ok.
E
D
F
Construct the perpendicular bisector for each side of
DEF.
DE then go to the drop-down menu Construct – Midpoint.
Construct the midpoint of EF and DF . (It is not necessary to label the
3. Highlight
midpoints)
4. Highlight DE and the midpoint of DE then go to the drop-down menu
Construct – Perpendicular. We should also change the color and style of the
perpendicular line we just created. Display – Color – Red then Display – Line
Style – Dashed. Construct the perpendicular bisectors of
Geometry – Triangles
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EF and DF .
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E
F
D
Label the intersection of the perpendicular bisectors as Ci.
5. Using the Point Tool place a point on the intersection of the three perpendicular
bisectors.
6. Highlight the three perpendicular bisectors and the three midpoints then go to
the drop-down menu Display – Hide.
7. Discuss with your teacher how to save your sketch.
E
Ci
D
F
The three perpendicular bisectors are concurrent at a point called the
circumcenter (Ci).
We are going to investigate some characteristics of the circumcenter.
Geometry – Triangles
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Questions
1. Highlight point E and move point E around the screen. Notice the circumcenter
moves as well.
Measure one of the angles of the triangle by highlighting the vertices of the triangle
then go to the drop-down menu Measure – Angle. Determine where the
circumcenter lies when the triangle is acute, right, and obtuse.
Record your answers below:
Acute Triangle
Right Triangle
Obtuse Triangle
Circumcenter lies:
2. Using the segment tool, construct a segment from the circumcenter to D, from the
circumcenter to E and from the circumcenter to F.
Highlight each of the segments then using the drop-down menu Measure – Length.
Repeat for each of the 3 segments you constructed.
Record your answers below:
DCi
ECi
FCi
Length of segment
3. What can you conclude about the distance from the circumcenter to each of the
verticies of the triangle?
4. Highlight point E, move point E around the screen. Does your answer to the
previous question remain the same?
5. Using your Circle Tool, you are going to construct a circle with center Ci and
radius ECi.
When you construct the circle, what do you notice?
Geometry – Triangles
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4. Highlight point E, and move point E around the screen. Does your answer to the
previous question remains the same?
5. Summarize your findings on the perpendicular bisectors of a triangle and the
circumcenter.
6. Try this! Using a straightedge and compass, construct the perpendicular
bisectors of a triangle and locate the circumcenter.
Geometry – Triangles
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