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Mastering Perpendicular and Angle Bisectors in Geometry

In this chapter, students will delve into the concepts of perpendicular and angle bisectors. They will learn to prove and apply theorems related to these essential geometric constructions. The chapter includes vocabulary, warm-up exercises, and exploration of constructions, as well as detailed notes on the application of bisector theorems. Students will engage in finding distances and measures related to bisectors and practice writing equations for bisectors in the coordinate plane. This chapter aims to solidify understanding through various examples and exercises.

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Mastering Perpendicular and Angle Bisectors in Geometry

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  1. Geometry Chapter 5 Perpendicular and Angle Bisectors

  2. Learning Targets • Students will be able to… • Prove and apply theorems about perpendicular bisectors. • Prove and apple theorems about angle bisectors.

  3. Warm-up Draw 2 perpendicular lines. Draw an angle bisector. Draw 2 parallel lines.

  4. Go Over Chapter 4 Test Check grades, tests, and homework packets

  5. 5.1 Vocabulary X A B

  6. 5.1 Vocabulary X A B

  7. Construction

  8. Construction

  9. Construction

  10. Beyond just Construction

  11. 5.1 Notes X A B If Distance and Perpendicular Bisectors

  12. 5.1 Notes X Then A B If Distance and Perpendicular Bisectors

  13. Applying the Theorem and Converse Find the measure. 1. Find MN 2. Find BC 3. Find TU

  14. Theorems A C P B Distance and Angle Bisectors

  15. Theorems A C P B Distance and Angle Bisectors

  16. Applying the Angle Bisector Theorems Find the measure. 1. BC 2.

  17. Applying the Angle Bisector Theorems Find the measure. 3.

  18. Example 4: Writing Equations of Bisectors in the Coordinate Plane A. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(-1, 6) and B(3, 4). Step 1: Find the midpoint. Step 2: Find the slope of the perpendicular bisector (opp. reciprocal) Step 3: Write in point-slope form (use the midpoint as a point)

  19. Extra Practice

  20. Extra Practice

  21. Extra Practice

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