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Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter

Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter. Notes 29 – Section 5.1. Essential Learnings. Students will understand and be able to identify and use perpendicular bisectors in triangles.

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Properties of Perpendicular Bisector & Circumcenter Properties of Angle Bisectors & Incenter

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  1. Properties of Perpendicular Bisector & CircumcenterProperties of Angle Bisectors & Incenter Notes 29 – Section 5.1

  2. Essential Learnings • Students will understand and be able to identify and use perpendicular bisectors in triangles. • Students will understand and be able to identify and use angle bisectors in triangles.

  3. Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. B 5 5 A C 4 D 4

  4. Example 1 Find the measure of PQ. Q 3x+1 5x-3 P R S

  5. Vocabulary Concurrent lines – when three or more lines intersect at a common point called the point of concurrency. Point of concurrency

  6. Circumcenter The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle.

  7. Construct Circumcenter 1. Draw a triangle 2. Construct perpendicular bisectors of each side of the triangle. 3. Intersection of three bisectors is the circumcenter.

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

  9. Example 2 Find the measure of AD. A D 5 B C

  10. Example 3 Find the measure of ∠WYZ. X W 28° Y Z

  11. Example 4 Find the measure of QS. Q S P R

  12. Incenter The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from each side of the triangle.

  13. Construct Incenter 1. Draw a triangle 2. Construct the three angle bisectors of the triangle. 3. Intersection of three angle bisectors is the incenter. The incenter is equidistant from each side.

  14. Constructions • Equilateral Triangle • Regular Hexagon • Square

  15. Assignment Page 327: 1-3, 9-14, 21-24, 32-34 Constructions Worksheet Unit Study Guide 8

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