- Step 1 On a sheet of paper or wax paper, draw a large scalene acute triangle. Make the triangle as large as you can.
- Step 2 Fold to construct the three medians of each side of the triangle. *Bring the endpoints together and pinch to locate the midpoints, then construct the medians with your straightedge.
- Step 3 Repeat steps 1 and 2 for an obtuse scalene triangle.

- Step 1
Take the scalene acute triangle you constructed
in the previous investigation and label it
*ABC*, as shown below. Do not worry if your triangle is a different shape.

- Step 2
Label the three medians
*AF*,*BD*, and*CE*. Label the centroid*G*.

- Step 3 Use your compass to answer the following questions: Is the centroid the same distance from the vertices? From the three sides? Take a look at how the centroid divides each median into two parts. Is the centroid the midpoint of each median?
- Step 4 You should have answered
no to each question in Step 3. Now compare the small part
on each median to the big part on that median. With you
compass or another piece of wax paper, measure
*GF*. Compare*GF*with*AG*by seeing how many times you can mark off the distance*GF*on*AG*. (If, for example, you can mark off*GF*three times on*AG*, then*AG*is three times as long as*GF*.) How many times as long as*GF*is*AG*? - Step 5 Compare the lengths
of the parts of the other two medians. (Segment
*BG*is how many times as long as*GD*? Segment*CG*is how many times as long as*GE*?)

- Step 1 On a sheet of paper or wax paper, draw a large scalene acute triangle. Make the triangle as large as you can.
- Step 2 Fold to construct the three angle bisectors in each angle of the triangle. *At each the vertex of the triangle pinch to locate the position of the angle bisector, then construct the angle bisectors with your straightedge.
- Step 3 Repeat steps 1 and 2 for an obtuse scalene triangle.

- Step 1
Take the scalene acute triangle you constructed
in the previous investigation and label it
*ABC*, as shown below. Do not worry if your triangle is a different shape.

- Step 2
Label the three angle bisectors
*AF*,*BD*, and*CE*. Label the incenter*I*.

- Step 3 Use your compass to answer the following questions: Is the incenter the same distance from the vertices? From the three sides? Take a look at how the incenter divides each bisector into two parts. Is the incenter the midpoint of each bisector?
- Step 4 The incenter is not the same distance from the vertices, but it is the same distance from the three sides. The incenter is not the midpoint of each bisector.