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GEOMETRY HELP Use the map of Washington, D.C. Describe the set of points that are equidistant from the Lincoln Memorial and the Capitol. The Converse of the Perpendicular Bisector Theorem states If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. Bisectors in Triangles LESSON 5-2 Additional Examples

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GEOMETRY HELP (continued) A point that is equidistant from the Lincoln Memorial and the Capitol must be on the perpendicular bisector of the segment whose endpoints are the Lincoln Memorial and the Capitol. Therefore, all points on the perpendicular bisector of the segment whose endpoints are the Lincoln Memorial and the Capitol are equidistant from the Lincoln Memorial and the Capitol. Quick Check Bisectors in Triangles LESSON 5-2 Additional Examples

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GEOMETRY HELP Find x, FB, and FD in the diagram above. FD = FB Angle Bisector Theorem 7x – 37 = 2x + 5 Substitute. 7x = 2x + 42 Add 37 to each side. 5x = 42 Subtract 2x from each side. x = 8.4 Divide each side by 5. FB = 2(8.4) + 5 = 21.8 Substitute. FD = 7(8.4) – 37 = 21.8 Substitute. Bisectors in Triangles LESSON 5-2 Additional Examples Quick Check

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Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side Theorem 5.1 Any point.

Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side Theorem 5.1 Any point.

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