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7F Constructing Perpendicular Bisectors You will need • • • • a ruler paper for folding a protractor a transparent mirror • a compass GOAL Investigate methods of constructing a perpendicular bisector of a segment. Explore the Math Chang is exploring methods of constructing a perpendicular bisector. ? How can you construct a perpendicular bisector? A. Draw segment EF. Fold the paper so that half the segment is exactly over the other half. Unfold the paper. Draw a line along the fold. B. Measure segment EF and each segment created. Mark the equal lengths. Predict the measure of each angle created. Check your prediction. Mark the right angles. C. Draw segment LM. Use a transparent mirror to construct the line of symmetry. Why is the line of symmetry the perpendicular bisector of segment LM? perpendicular bisector a line that divides a segment into two congruent segments and meets or crosses the segment at right angles D. Mark the equal lengths and right angles. E. Draw segment ST. Adjust a compass so that the distance between the pencil tip and compass point is greater than half the length of segment ST. With the compass point on point S, draw arcs above and below segment ST. F. Keep the distance between the pencil tip and compass point the same as in step E. With the compass point on point T, draw arcs above and below segment ST to intersect with the other arcs. C S T A B D S CD is the perpendicular bisector of AB. Equal segments are marked with the same number of tick marks. Right angles are marked as square corners. T G. Join the points where the arcs intersect. Mark the equal lengths and right angles. Reflecting 1. In step E, why is it necessary to make the distance between the pencil tip and compass point greater than half the length of segment ST? 2. How is a perpendicular bisector of a segment the same as a line of symmetry? 3. The measure of a straight angle along a segment is 180º. Why is each angle formed by a perpendicular bisector a right angle? 4. How do your constructions show the meaning of a perpendicular bisector? 88 Chapter 7: 2-D Geometry Copyright © 2006 by Thomson Nelson