5 2 Use Perpendicular Bisectors Theorem 5 2

5. 2 Use Perpendicular Bisectors 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. A C P B

5. 2 Use Perpendicular Bisectors 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 A ______ of the segment. C P D B

5. 2 Use Perpendicular Bisectors Example 1 Use the Perpendicular Bisector Theorem AC is the perpendicular bisector of BD. Find AD. Solution B 7 x – 6 C A 4 x D

5. 2 Use Perpendicular Bisectors Example 2 Use perpendicular bisectors In the diagram, KN is the perpendicular bisector of JL. a. What segment lengths in the diagram are equal? b. Is M on KN? Solution K N J 13 L 13 a. KN bisects JL, so ____ = ____. Because K is on the perpendicular bisector M of JL, ____ = ____ by the Theorem 5. 2. The diagram shows that ____ = 13. equidistant from J and L. b. Because MJ = ML, M is ______ of the Perpendicular Bisector Theorem So, by the Converse _____________________, M is on the perpendicular bisector of JL, which is KN.

5. 2 Use Perpendicular Bisectors Checkpoint. In the diagram, JK is the perpendicular bisector of GH. F 1. What segment lengths are equal? 4. 1 J 2. Find GH. G K 2 x x+1 H

5. 2 Use Perpendicular Bisectors 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. B D A If PD, PE, and PF are perpendicular bisectors, then PA = _____. P F E C

5. 2 Use Perpendicular Bisectors Example 3 Use the concurrency of perpendicular bisectors N 1. The perpendicular bisectors of MNO meet at point S. Find SN. 7 Q P Solution S 9 M 2 R Using _______, you know that point S is Theorem 5. 4 _______ equidistant from the vertices of the triangle. So, _____ = _____ Theorem 5. 4. Substitute. O

5. 2 Use Perpendicular Bisectors Checkpoint. Complete the following exercise. 3. The perpendicular bisector of ABC meet at point G. Find GC. B 12 By _______, Theorem 5. 4 D _____ = _____. E G 15 A 6 F C

5. 2 Use Perpendicular Bisectors Pg. 284, 5. 2 #1 -10