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Warm Up

Use Perpendicular Bisectors. Warm Up. Lesson Presentation. Lesson Quiz. 3. If M is the midpoint of AB , AM = 5 x – 2, and MB = 3 x + 6, find AB. 3. ANSWER. 36. ANSWER. 8.5. ANSWER. Warm-Up. 1. Solve 3 x = 8 x – 15. 2. Solve 6 x + 3 = 8 x – 14.

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Warm Up

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  1. Use Perpendicular Bisectors Warm Up Lesson Presentation Lesson Quiz

  2. 3.If M is the midpoint ofAB, AM = 5x – 2, andMB = 3x + 6,find AB. 3 ANSWER 36 ANSWER 8.5 ANSWER Warm-Up 1.Solve 3x = 8x – 15. 2.Solve 6x + 3 = 8x – 14.

  3. BDis the perpendicular bisector of AC. Find AD. ALGEBRA 3x + 14 5x= x = 7 5x = 35 AD = 5(7) = Example 1 SOLUTION AD=CD Perpendicular Bisector Theorem Substitute. Solve for x.

  4. In the diagram, WXis the perpendicular bisector of YZ. a. What segment lengths in the diagram are equal? a. WXbisects YZ , so XY =XZ. Because Wis on the perpendicular bisector of YZ, WY =WZby Theorem 5.2. The diagram shows that VY = VZ = 25. Example 2 SOLUTION

  5. In the diagram, WXis the perpendicular bisector of YZ. Because VY = VZ,Vis equidistant from Yand Z. So, by the Converse of the Perpendicular Bisector Theorem, Vis on the perpendicular bisector of YZ, which is WX. b. IsV onWX ? b. Example 2 SOLUTION

  6. In the diagram, JKis the perpendicular bisector of NL. 1. What segment lengths are equal? Explain your reasoning. ANSWER NJ =LJsince JKbisects NL. NK = LK by the Perpendicular Bisector Theorem and the diagram shows ML =MN. Guided Practice

  7. In the diagram, JKis the perpendicular bisector of NL. 2. Find NK. ANSWER 13 Guided Practice

  8. In the diagram, JKis the perpendicular bisector of NL. Explain why Mis on JK. 3. ANSWER Since ML = MN, Mis equidistant from Nand L, so by the Converse of the Perpendicular Bisector Theorem Mis on the perpendicular bisector of NLwhich is JK. Guided Practice

  9. Example 3 FROZEN YOGURT Three snack carts sell frozen yogurt from points A, B, and Coutside a city. Each of the three carts is the same distance from the frozen yogurt distributor. Find a location for the distributor that is equidistant from the three carts.

  10. Copy the positions of points A, B, and Cand connect those points to draw ABC. Then use a ruler and protractor to draw the three perpendicular bisectors of ABC. The point of concurrency Dis the location of the distributor. Example 3 SOLUTION Theorem 5.4 shows you that you can find a point equidistant from three points by using the perpendicular bisectors of the triangle formed by those points.

  11. ANSWER Where the perpendicular bisectors of the triangle formed by A, B, and Eintersect Guided Practice Hot pretzels are sold from points Aand Band also from a cart at point E. Where could the pretzel distributor be located if it is equidistant from those three points? Sketch the triangle and show the location. WHAT IF? 4.

  12. 1. ANSWER 25 Lesson Quiz In Exercises 1 and 2, find AB.

  13. 2. ANSWER 24.5 Lesson Quiz In Exercises 1 and 2, find AB.

  14. 3. In this diagram, the perpendicular bisectors of ABC meet at point G. Find EC and GC. ANSWER 5; 7 Lesson Quiz

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