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1.5 segs __angle_bisectors

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  • 1. 1.5 Segment & Angle Bisectors p.34
  • 2. Always Remember!• If they are congruent, then set their measures equal to each other!
  • 3. Midpoint• The point that bisects a segment.• Bisects? splits into 2 equal pieces 12x+3 10x+5 A M B 12x+3=10x+5 2x=2 x=1
  • 4. Segment Bisector• A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B
  • 5. Compass & Straightedge• Tools used for creating geometric constructions• We will do a project with these later.
  • 6. Midpoint Formula• Used for finding the coordinates of the midpoint of a segment in a coordinate plane.• If the endpoints are (x1,y1) & (x2,y2), then  x1 + x2 y1 + y2   ,   2 2 
  • 7. Ex: Find the midpoint of SP if S(-3,-5) & P(5,11).  − 3 + 5 − 5 +11   ,   2 2  2 6   ,  2 2  (1,3)
  • 8. Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.  x1 + x2 y1 + y2   ,  = (midpoint )  2 2  x1 + x2 y1 + y2 =2 =4 2 2 − 1 + x2 7 + y2 =2 =4 2 2 − 1 + x2 = 4 7 + y2 = 8 x2 = 5 y2 = 1 ( 5,1)
  • 9. Angle Bisector• A ray that divides an angle into 2 congruent adjacent angles. A D BD is an angle bisector of <ABC.B C
  • 10. Ex: If FH bisects <EFG &m<EFG=120o, what is m<EFH? E 120 H = 60 o 2 F G m < EFH = 60 o
  • 11. Last example: Solve for x. * If they are congruent, set them equal to each other, then solve! o 0 x +4 x+40=3x-20 o 3x-20 40=2x-20 60=2x 30=x
  • 12. Assignment

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