1. 3.1 Duplicating Segments and Angles “It is only the first step that is difficult” Marie De Vichy-Chamrod

2. 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.

3. Sketch, Draw, Construct 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 triangle that looks like an equilateral triangle. No geometry tools needed. When you ___________ an equilateral triangle with a compass and straightedge, you don’t rely on measurements from a protractor or a ruler. This guarantees that you triangle is equilateral. draw sketch construct

4. Investigation 1 Copying a Segmentp 143 Copying a Segment

5. Investigation 2 Copying an Anglep 144 Copying an Angle

6. 3.2 Constructing Perpendicular Bisectors “ To be successful, the first thing to do is to fall in love with your work.” Sister Mary Lauretta

7. Objectives Discover a method of constructing perpendicular bisectors and midpoints. Make conjectures about perpendicular bisectors.

8. Definitions ____________________: A line, ray, or segment in a plane that passes through the midpoint of a segment in a plane. ____________________: A line, ray, or segment in a plane that cuts a line segment into two equal parts at 90°. ____________________: The segment connecting the vertex of a triangle to the midpoint of its opposite side. ____________________: The segment that connects the midpoint of two sides of a triangle. Midsegment Segment Bisector Perpendicular Bisector Median

9. Investigation 1 Finding the Right BisectorP. 147 Perpendicular Bisector Conjecture If a point is on the perpendicular bisector of a segment, then it is ____________ from the endpoints. Perpendicular Bisector equidistant

10. Investigation 2 Right Down the MiddleP. 148 Converse of the Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the ______________________ of the segment. perpendicular bisector