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5.2: Bisectors in Triangles

5.2: Bisectors in Triangles. Objectives: To use properties of perpendicular and angle bisectors. Warm Up. What is a perpendicular bisector of a segment? What is an angle bisector? What does equidistant mean?. is the perpendicular bisector of What do we know?.

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5.2: Bisectors in Triangles

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  1. 5.2: Bisectors in Triangles Objectives: To use properties of perpendicular and angle bisectors

  2. Warm Up • What is a perpendicular bisector of a segment? • What is an angle bisector? • What does equidistant mean?

  3. is the perpendicular bisector of What do we know?

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

  5. Converse of Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. IS THE PERPENDICULAR BISECTOR OF SEGMENT AB 6 6

  6. EXAMPLES • Find PB and AQ. 14 7

  7. Find AD, x, and BC. 12 C D A 2x+6 3x+1 B

  8. What do we know about P? 10 10

  9. Definition The distance from a point to a line is defined as the length of the perpendicular segment from the point to the line.

  10. Angle Bisector Theorem • If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. 4 4

  11. Converse of 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.

  12. Let’s try an example… • Solve for x. Then find AD & CD. 5x = 2x + 24 3x = 24 X = 8 AD=5*8=40 CD=2*8+24=40 5x 2x + 24

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