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Objectives: Use properties of perpendicular and angle bisectors to solve problems

Section 5-2 Triangle Bisectors SPI 32J: identify the appropriate segment of a triangle given a diagram (median, altitude, angle, perpendicular bisector). Objectives: Use properties of perpendicular and angle bisectors to solve problems. Recall.

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Objectives: Use properties of perpendicular and angle bisectors to solve problems

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  1. Section 5-2 Triangle Bisectors SPI 32J: identify the appropriate segment of a triangle given a diagram (median, altitude, angle, perpendicular bisector) • Objectives: • Use properties of perpendicular and angle bisectors to solve problems Recall • Perpendicular • line segment that forms a right angle to another line segment • Bisector • divides a line (or angle) into two congruent parts

  2. Perpendicular Bisector Theorem Theorem 5-2 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

  3. Converse of the Perpendicular Bisector Theorem Thm 5-3 Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. 10m 10m

  4. Bisectors of Triangles Thm 5-4 Angle Bisector Theorem If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Thm 5-5 Converse of the Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

  5. Apply Bisectors of Triangles Find x, FB, and FD in the diagram. Justify your answers. FD = FB Angle Bisector Theorem 7x – 37 = 2x + 5Substitute. 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.

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