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MAZZEO/PRIZIO GEOMETRY Period__Date__/__/__Name______________________________ Lesson 3.1 How do we construct a perpendicular bisector and construct an inscribed square? Do BREAKING NEWS: A bisector cuts a segment or angle into two congruent parts. Now Read the following and underline the statements that you understand and circle the statements that are confusing. Given: Points X, Y, and Z are collinear. Line AY bisects segment XZ such that a right angle is formed. Draw a diagram to illustrate this situation. Be sure to label thoroughly. What I know: What I wonder: How can I cope with these moments of confusion? STOP! Bisector: A perpendicular bisector of a segment passes through the Perpendicular 1. Place your compass point on A and stretch the compass MORE THAN half way to point B, but not beyond B. _________________ AND 2. With this length, swing a large arc that will forms _________________ with the segment. go BOTH above and below . (If you do not wish to make one large continuous arc, you may simply place one small arc above below Directions for constructing a Perpendicular Bisector can be found here (follow the arrows) and one small arc .) 3. Without changing the span on the compass, place the compass point on B and swing the arc again. The two arcs you have created should intersect. 4. With your straightedge, connect the two points of intersection. 5. This new straight line bisects Using the directions and visual provided in class, construct a perpendicular bisector of the segment below. . Label the point where the new line and cross as C. 6. has now been bisected and AC = CB. (It could also be said that the segments are congruent, .) Let’s try it again. Using only a compass and a straightedge, construct the perpendicular bisector of and label it c. [Leave all construction marks.] Now that you are familiar with the construction of a perpendicular bisector, we must make one last observation. Using your compass, examine the following pair of segments. NEW CONSTRUCTIONS: Inscribed Square: Here are the steps for an Inscribed Square… How to construct an inscribed square? The construction proceeds as follows: 1. Construct a circle and mark the center point. Make it nice and bold. 2. KEEP THE RADIUS THE SAME. 3. Using a straightedge, draw a diameter. 4. Construct a perpendicular bisector of the diameter. The perpendicular bisector is also a diameter of the circle. 5. The resulting four points on the circumference of the circle are the vertices of the inscribed square. 6. Connect these four points using a straightedge and there is your square! Try it below! SUMMARY: When I don’t understand a direction a strategy (or strategies) that help me is …