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5-1 Bisectors of Triangles

5-1 Bisectors of Triangles. You used segment and angle bisectors. Identify and use perpendicular bisectors in triangles. Identify and use angle bisectors in triangles. Perpendicular Bisector. K. R. S. J.

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5-1 Bisectors of Triangles

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  1. 5-1 Bisectors of Triangles You used segment and angle bisectors. • Identify and use perpendicular bisectors in triangles. • Identify and use angle bisectors in triangles.

  2. Perpendicular Bisector K R S J Perpendicular bisector is any segment that intersects another segment at its midpoint AND is perpendicular to that segment.

  3. Perpendicular Bisector • A perpendicular bisector of a side of a triangle is a line perpendicular to a side through the midpoint of the side. • (Perpendicular and bisects one side only) Perpendicular bisector B C A

  4. Page 324

  5. A. Find BC. BC = AC Perpendicular Bisector Theorem BC = 8.5 Substitution Answer:8.5

  6. B. Find XY. Answer:6

  7. C. Find PQ. PQ = RQ Perpendicular Bisector Theorem 3x + 1 = 5x – 3 Substitution 1 = 2x – 3 Subtract 3x from each side. 4 = 2x Add 3 to each side. 2 = x Divide each side by 2. So, PQ = 3(2) + 1 = 7. Answer:7

  8. A. Find NO. A. 4.6 B. 9.2 C. 18.4 D. 36.8

  9. B. Find TU. A. 2 B. 4 C. 8 D. 16

  10. Definitions Concurrent lines – three or more lines intersect at a common point. Point of concurrency – the point where concurrent lines intersect. The point of concurrency is also called the circumcenter of the triangle

  11. Concurrent Lines • If three or more coplanar lines intersect at the same point, they are concurrent lines. • The point of intersection is the point of concurrency. Concurrent lines Point of concurrency

  12. Page 325

  13. Page326

  14. A D B C Angle Bisector • When an angle bisector is used in a triangle, it is a segment. The angle bisector cuts the angle in half and goes to the other side. Angle bisector

  15. Page 327

  16. A. Find DB. DB = DC Angle Bisector Theorem DB = 5 Substitution Answer:DB = 5

  17. C. Find QS. QS = SR Angle Bisector Theorem 4x – 1 = 3x + 2 Substitution x – 1 = 2 Subtract 3x from each side. x = 3 Add 1 to each side. Answer:So, QS = 4(3) – 1 or 11.

  18. A. Find the measure of SR. A. 22 B. 5.5 C. 11 D. 2.25

  19. B. Find the measure of HFI. A. 28 B. 30 C. 15 D. 30

  20. C. Find the measure of UV. A. 7 B. 14 C. 19 D. 25 **Set equal to each other

  21. Page 328

  22. A. Find the measure of GF if D is the incenter of ΔACF. A. 12 B. 144 C. 8 D. 65 **Use Pythagorean Theorem

  23. B. Find the measure of BCD if D is the incenter of ΔACF. A. 58° B. 116° C. 52° D. 26°

  24. 5-1 Assignment Page 329, 2-30 even, skip 4

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