In this investigation on The Geometer's Sketchpad you will construct the four centers of a given triangle.

On a new sketch.

Step 1 Construct and label trinagle ABC.
Step 2 Construct the bisectors of angle A and angle B.
Step 3 Construct the intersection point of the two lines, label this point incenter.
Step 4 Hide the angle bisectors.
Step 5 Construct the perpendicular bisectors of two sides.
Step 6 Construct the intersection point of the two lines, label this point circumcenter.
Step 7 Hide the perpendicular bisectors.
Step 8 Construct the altitudes of angle A and angle B.
Step 9 Construct the intersection point of the two lines, label this point orthocenter.
Step 10 Hide the altitudes.
Step 11 Construct the midpoints of the sides.
Step 12 Construct the median from point A to the midpoint of segment BC.
Step 13 Construct the median from point B to the midpoint of segment AC.
Step 14 Construct the intersection point of the medians and label it centroid.
Step 15 Hide the medians.


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