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Do Now

Do Now. Take a protractor from the front. Take out your compass. Draw an obtuse angle. Construct (using only a compass and straightedge) a duplicate angle. . Perpendicular bisectors. Perpendicular Bisectors—Terms.

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Do Now

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  1. Do Now • Take a protractor from the front. • Take out your compass. • Draw an obtuse angle. • Construct (using only a compass and straightedge) a duplicate angle.

  2. Perpendicular bisectors

  3. Perpendicular Bisectors—Terms • A segment bisector—a line, ray, or segment that passes through the midpoint of a segment. • Cuts the line segment in half • Perpendicular lines—intersect at a right angle. • Perpendicular bisector—passes through the midpoint of a segment at a right angle. • Equidistant—the same distance

  4. Constructing Perpendicular Bisectors • Step 1: Draw a line segment. Set your compass to more than half the distance between the two endpoints. • Step 2: Using one endpoint as center, swing an arc on both sides of the segment. • Step 3: Using the same compass setting, swing an arc from the other endpoint to intersect each arc. • Step 4: Mark your two intersection points and connect them.

  5. Perpendicular Bisector Conjecture • If a point is on the perpendicular bisector of a segment, then it is _________ from the endpoints. • equidistant

  6. Converse of Perpendicular Bisector Conjecture • If a point is equidistant from the endpoints of a segment, then it is on the _______________of the segment. • perpendicular bisector • Also true!

  7. Practice • Draw and label AB. Construct the perpendicular bisector of AB.

  8. Practice • Draw and label QD. Construct perpendicular bisectors to divide QD into four congruent segments.

  9. Perpendicular Postulate • If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

  10. Exploring Slopes • Slope of Line 1? • Slope of Line 2?

  11. Slopes of Parallel Lines • Parallel Lines have equal slopes

  12. Equations of Parallel Lines • Are these lines parallel? • y=3x + 8 • y=3x – 4 • How do you know?

  13. Slopes of Perpendicular Lines • Perpendicular lines have opposite reciprocal slopes.

  14. Equations of Perpendicular Lines • Are these lines perpendicular? • y= 5x + 7 • y= 5x – 2 • NO! • y= ½ x – 3 • y= - ½ x – 9 • NO! • y= ¼ x • y= 4x + 7 • NO! • y= -⅓x + 2 • y= 3x – 4

  15. Derive the Expression for Slopes of Perpendicular Lines • 3 • 1/6 • -8 • -1/2 • 3/4 • -t • a/b • m

  16. Stations! • Direct: Practice • Collaborative: Without writing on the worksheets, complete 3.1 worksheet on a separate sheet of paper as a group. (Each person turn in your own paper.) DO NOT WRITE ON IT! • Independent: Take your test and your notebook and begin test corrections. If you are satisfied with your test score, begin vocabulary that is due on Wednesday.

  17. Practice

  18. Today’s Objectives • Duplicate a line segment, an angle and a polygon • Construct perpendicular bisectors and midpoints • Make conjectures about perpendicular bisectors • Use Problem Solving skills

  19. Exit Slip For all exercises, do not erase your construction marks. • Draw an obtuse angle. Label it ∠LGE, then duplicate it. • Draw a line segment. Label it RS, then duplicate it. • Draw a line segment. Label it PQ, then construct its perpendicular bisector. • Line segment AB starts at A (1, 2) and ends at B (4, 0). Line segment CD starts at C (.5, -2) and ends at D (4.5, 4). • Determine if these lines are perpendicular bisectors. • Explain your reasoning.

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