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Chapter 5 Relationships Within Triangles

Chapter 5 Relationships Within Triangles. 5-2 Bisectors in Triangles. Perpendicular Bisectors and Angle Bisectors. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Perpendicular Bisector Theorem.

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Chapter 5 Relationships Within Triangles

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  1. Chapter 5 Relationships Within Triangles 5-2 Bisectors in Triangles

  2. Perpendicular Bisectors and Angle Bisectors • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Perpendicular Bisector Theorem

  3. Perpendicular Bisector Theorem Proof Given: A is on the perpendicular bisector of XY. Prove: A M X Y Given A is on the perpendicular bisector of XY. Definition of Segment Bisector Definition of Perpendicular Bisector All Right Angles are Congruent Reflexive SAS CPCTC

  4. 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.

  5. CD is the perpendicular bisector of AB. Find CA and DB. C 5 5 A B 6 6 D

  6. Distance from a point to a line The distance from a point to a line is the perpendicular segment from the point to the line. In the diagram, is the bisector of ∠CAB. If you measure the lengths of the perpendicular segments from D to the sides of the angle you will find that the lengths are equal so D is equidistant from the sides. C D A B

  7. Angle Bisector Theorem • If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. C D A B

  8. 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. C D A B

  9. Using the Angle Bisector Theorem • What is the length of FD? C B D 5x 2x+24 F 5x = 2x + 24 3x = 24 x = 8

  10. a. 10 10 b. It is the angle bisector of angle E 2x = x + 20 x = 20 d. 80

  11. Pg. 267 #1-4, 6-26, 51-53, 56-64

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