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Geometry Chapter 1 1.06: Compasses, Angles, and Circles Diagram: Name ________________________ Perpendicular Bisector Theorem Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment. Converse: If a point is equidistant from the 2 end points of a segment, then the point lies on its perpendicular bisector. Task #1: Construct the three medians of the triangle. Median Diagram: Definition: a segment that connects a vertex of a triangle to the midpoint of the opposite side Task #2: Construct the three midlines of the triangle. Midline Diagram: Definition: a segment that connects the midpoints of 2 sides of a triangle Task #3: Construct the three angle bisectors of the triangle. Angle Bisector Diagram: Definition: line that divides an angle into 2 congruent (equal) angles. Q: After your construction, what do you notice about these lines and their opposite sides? Task #4: Construct the three altitudes of the triangle. Altitude Diagram: Definition: perpendicular segment from a vertex of a triangle to a line that CONTAINS the opposite side Q: How do we construct the altitude from the vertex on the top?!