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Lesson 5–1 Objectives

Lesson 5–1 Objectives. Be able to prove and apply theorems about  bisectors Be able to prove and apply theorems about  bisectors. State HSCE:. Equidistant – when a point is the same distance away from two objects. X. A. B. Point X is equidistant from points A and B.

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Lesson 5–1 Objectives

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  1. Lesson 5–1 Objectives • Be able to prove and apply theorems about  bisectors • Be able to prove and apply theorems about  bisectors

  2. State HSCE:

  3. Equidistant – when a point is the same distance away from two objects X A B Point X is equidistant from points A and B

  4. Proof of  Bisector Theorem

  5. Applying  Bisector Thm & Conv. What do you know about TU & VU? What’s the reason? Find TU. TU = UV  Bisector Thm. 3x + 9 = 7x – 17 Substitute the given values. 9 = 4x – 17 Subtract 3x from both sides. 26 = 4x Add 17 to both sides. 6.5 = x Divide both sides by 4. So TU = 3(6.5) + 9 = 28.5.

  6. Applying  Bisector Thm & Conv. What do you know about BD & CD? What’s the reason? BD = CD by Conv of  Bis Thm Find BC. BC = 2CD Def. of seg. bisector. BC = 2(12) = 24 Substitute 12 for CD.

  7. Applying Bisector Thm & Conv. What do you know about KM? What’s the reason? KM is the  Bisector Find mMKL mMKL = mJKM Def. of  bisector 3a + 20 = 2a + 26 Substitute the given values. a + 20 = 26 Subtract 2a from both sides. a= 6 Subtract 20 from both sides. So mMKL = [2(6) + 26]° = 38°

  8. It is given that . So D is on the perpendicular bisector of by the Converse of the Angle Bisector Theorem. Since B is the midpoint of , is the perpendicular bisector of . Therefore the spotlight remains centered under the mounting. John wants to hang a spotlight from a rafter (AC). The wires AD and CD are the same length. How do you know the spotlight will be centered?

  9. Lesson 5–1 Assignment

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