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Bisectors of Triangles

5.1. Bisectors of Triangles. Assignment 7 : 5.1 WB Pg. 59 #1 – 6 all WB Pg . 60 #1 – 6 all. Holt Geometry. 5.1. Bisectors of Triangles.

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Bisectors of Triangles

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  1. 5.1 Bisectors of Triangles Assignment 7: 5.1 WB Pg. 59 #1 – 6 all WB Pg. 60 #1 – 6 all Holt Geometry

  2. 5.1 Bisectors of Triangles A perpendicular bisectoris a combination of an altitude and a median. It is a line (ray or segment) that is perpendicular to the segment at its midpoint.

  3. 5.1 Bisectors of Triangles 5 - 1 5 - 2

  4. 5.1 Bisectors of Triangles 5 - 4 5 - 5

  5. Since AB = AC and , is the perpendicular bisector of by the Converse of the Perpendicular Bisector Theorem. 5.1 Bisectors of Triangles Example 1: Applying the Perpendicular Bisector Theorem and Its Converse Find each measure. BC BC = 2CD Def. of seg. bisector. BC = 2(12) = 24 Substitute 12 for CD.

  6. 5.1 Bisectors of Triangles Example 2: Applying the Perpendicular Bisector Theorem and Its Converse Find each measure. 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.

  7. Since EH = GH, and , bisects EFGby the Converse of the Angle Bisector Theorem. 5.1 Bisectors of Triangles Example 3: Applying the Angle Bisector Theorem Find the measure. mEFH, given that mEFG= 50°. Def. of  bisector Substitute 50° for mEFG.

  8. Since, JM = LM, and , bisects JKL by the Converse of the Angle Bisector Theorem. 5.1 Bisectors of Triangles Example 4:Applying the Angle Bisector Theorem 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°

  9. Use the diagram for Items 3–4. 3. Given that FH is the perpendicular bisector of EG, EF = 4y – 3, and FG = 6y – 37, find FG. 4. Given that EF = 10.6, EH = 4.3, and FG = 10.6, find EG. 5.1 Bisectors of Triangles Lesson Practice Use the diagram for Items 1–2. 1. Given that mABD = 16°, find mABC. 2. Given that mABD = (2x + 12)° and mCBD = (6x – 18)°, find mABC. 32° 54° 65 8.6

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