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5.2

5.2. Use Perpendicular Bisectors. C. A. B. P. Theorem 5.2: Perpendicular Bisector Theorem. In a plane, if a point is on the perpendicular bisector of a segment, then it is __________ from the endpoints of the segment. 5.2. Use Perpendicular Bisectors. C. A. B. P. D.

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5.2

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  1. 5.2 Use Perpendicular Bisectors C A B P Theorem 5.2: Perpendicular Bisector Theorem In a plane, if a point is on the perpendicular bisector of a segment, then it is __________ from the endpoints of the segment.

  2. 5.2 Use Perpendicular Bisectors C A B P D Theorem 5.3: Converse of the Perpendicular Bisector Theorem In a plane, if a point is equidistant from the endpoints of a segment, then it is on the ____________ _________ of the segment.

  3. 5.2 Use Perpendicular Bisectors B 7x – 6 C A 4x D Use the Perpendicular Bisector Theorem Example 1 AC is the perpendicular bisector of BD. Find AD. Solution

  4. 5.2 Use Perpendicular Bisectors K N L J 13 13 M Use perpendicular bisectors Example 2 In the diagram, KN is the perpendicular bisector of JL. • What segment lengths in the diagram are equal? • Is M on KN? Solution • KN bisects JL, so ____ = ____. Because K is on the perpendicular bisector of JL, ____ = ____ by the Theorem 5.2. The diagram shows that ____ = ____ = 13. equidistant • Because MJ = ML, M is ____________ from J and L. So, by the __________________________________________, M is on the perpendicular bisector of JL, which is KN. Converse of the Perpendicular Bisector Theorem

  5. 5.2 Use Perpendicular Bisectors F 4.1 4.1 J H K G 2x x + 1 Checkpoint. In the diagram, JK is the perpendicular bisector of GH. • What segment lengths are equal? • Find GH.

  6. 5.2 Use Perpendicular Bisectors B C A E D P F If PD, PE, and PF are perpendicular bisectors, then PA = _____ = _____. Theorem 5.4: Concurrency of Perpendicular Bisector of a Triangle The perpendicular bisector of a triangle intersects at a point that is equidistant from the vertices of the triangle.

  7. 5.2 Use Perpendicular Bisectors The perpendicular bisectors of MNO meet at point S. Find SN. N 7 Q P S O 9 2 R M Use the concurrency of perpendicular bisectors Example 3 Solution Using ______________, you know that point S is _____________ from the vertices of the triangle. Theorem 5.4 equidistant So, _____ = _____ = _____. _____ = _____ Theorem 5.4. _____ = _____ Substitute.

  8. 5.2 Use Perpendicular Bisectors • The perpendicular bisector of ABC meet at point G. Find GC. B 12 D E G 15 6 A C F Checkpoint. Complete the following exercise. By ______________, Theorem 5.4 _____ = _____ = _____.

  9. 5.2 Use Perpendicular Bisectors Pg. 284, 5.2 #1-10

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