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LESSON 5-2 BISECTORS IN TRIANGLES

LESSON 5-2 BISECTORS IN TRIANGLES. OBJECTIVE: To use properties of perpendicular bisectors & angle bisectors. NO, NOT . YES, DISTANCE. The distance from a point to a line. is the length of the perpendicular segment from the point to the line. THEOREM 5-2

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LESSON 5-2 BISECTORS IN TRIANGLES

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  1. LESSON 5-2 BISECTORS IN TRIANGLES OBJECTIVE: To use properties of perpendicular bisectors & angle bisectors

  2. NO, NOT  YES, DISTANCE The distance from a point to a line is the length of the perpendicular segment from the point to the line.

  3. THEOREM 5-2 PERPENDICULAR BISECTOR THEOREM If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. IF THEN

  4. A THEOREM 5-3 PERPENDICULAR BISECTOR THEOREM(Converse) If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. THEN IF A

  5. Example 1: Find CA and DB. Explain. C 5cm CA = 5cm A B DB = 6cm 6cm D REASON: C and D are on the perpendicular bisector of AB

  6. THEOREM 5-4 ANGLE BISECTOR THEOREM If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.. THEN IF

  7. THEOREM 5-5 ANGLE BISECTOR THEOREM (Converse) If a point is in the interior of an angle and is equidistant from the sides of the angle, then the point is on the angle bisector. THEN IF

  8. C B D E A 5x 2x + 24 F Example #2 Find the value of x. Then find FA and FE. 5x = 2x + 24 3x = 24 x = 8 FA = 5(8) = 40

  9. C B D E A 5x 2x + 24 F FA = FE Why? A point on an angle bisector is equidistant from the sides of the angle.

  10. ASSIGNMENT: Page 251 #1-26, 41-42, 55-57 Write algebraic equations for #6, 7, 9, 55, 56, 57 Write out the thms for 5, 8, 17, 26

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