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3.1 Duplicating Segments and Angles “It is only the first step that is difficult” Marie De Vichy-Chamrod Objectives • Introduce geometric constructions with straightedge, compass, and patty paper. • Distinguish among construction, sketches, and drawings of geometric figures. • Discover construction methods to duplicate a segment, an angle, and a polygon. Sketch, Draw, Construct draw When you ___________ an equilateral triangle, you should use you geometry tools for accuracy. You may use a protractor to measure angles and a ruler to measure the sides. When you ___________ an equilateral triangle, you freehand a sketch triangle that looks like an equilateral triangle. No geometry tools needed. When you ___________ an equilateral triangle with a compass construct and straightedge, you don’t rely on measurements from a protractor or a ruler. This guarantees that you triangle is equilateral. Investigation 1 Copying a Segment Copying a Segment p 143 Investigation 2 Copying an Angle p 144 Copying an Angle 3.2 Constructing Perpendicular Bisectors “ To be successful, the first thing to do is to fall in love with your work.” Sister Mary Lauretta Objectives • Discover a method of constructing perpendicular bisectors and midpoints. • Make conjectures about perpendicular bisectors. Definitions ____________________: A line, ray, or segment in a plane that Segment Bisector passes through the midpoint of a segment in a plane. Perpendicular Bisector A line, ray, or segment in a plane that ____________________: cuts a line segment into two equal parts at 90°. Median ____________________: The segment connecting the vertex of a triangle to the midpoint of its opposite side. ____________________: The segment that connects the Midsegment midpoint of two sides of a triangle. Investigation 1 Finding the Right Bisector P. 147 Perpendicular Bisector Perpendicular Bisector Conjecture If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. ____________ Investigation 2 Right Down the Middle P. 148 Converse of the Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector ______________________ of the segment.
