Using a straightedge, draw any triangle ABC a)Label the intersection of the perpendicular bisectors as the circumcenter. b)Measure & label the distance from each vertex to the circumcenter. What do you notice? Define perpendicular bisector: Define circumcenter: Theorem:

Make a copy of triangle ABC from Construction 1 a)Label the intersection of the medians as the centroid. b)Measure & label the length of each median & the length from each vertex to the centroid. What do you notice? Define median of a triangle: Define centroid: Theorem:

a)Label the intersection of the altitudes as the orthocenter. Define altitude of a triangle: Define orthocenter: Make a copy of triangle ABC from Construction 1

a)Label the intersection of the angle bisectors as the incenter. b)Measure & label the length of each segment from the incenter to the edge of the triangle. What do you notice? Define angle bisector: Define incenter: Theorem: Make a copy of triangle ABC from Construction 1

Day 2 Cut out each triangle and try to balance each one on the tip of a pencil at each of the intersections. Which are possible? Which are not possible? Complete the each process for a different type of triangle. (Ex: obtuse, scalene, right, isosceles, etc.) Staple all triangles to their corresponding sheet & keep for a reference.