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1. If mFGH = 60, what is the value of x ?

1. If mFGH = 60, what is the value of x ? 2. From the information given in the figure, what is AC ?. Homework answers – p . 268 #8-13 and #21-26. #8. No; since CA is not equal to CB, C is not on the perpendicular bisector of segment AB #9 No; the diagram does not show that CA = CB

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1. If mFGH = 60, what is the value of x ?

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  1. 1. If mFGH = 60, what is the value of x? 2. From the information given in the figure, what is AC?

  2. Homework answers – p. 268 #8-13 and #21-26 #8. No; since CA is not equal to CB, C is not on the perpendicular bisector of segment AB #9 No; the diagram does not show that CA = CB #10 No; the diagram does not show that CA = CB #11. No; since P is not equidistant from the sides of angle A, P is not on the bisector of angle A #12. No; the diagram does not show that both of the segments with equal length are perpendicular segments #13. No; the diagram does not show that the segments with equal length are perpendicular segments #21. B #22. A #23. C #24. F #25. D #26. E

  3. Draw a triangle • Construct a perpendicular bisector to each side • Make a conjecture • Draw a triangle • Construct an angle bisector to each angle • Make a conjecture

  4. Lesson 5.2 Objective: Using perpendicular bisectors, and angle bisectors of a triangle

  5. Concurrent lines (or rays or segments): 3 or more lines (or rays or segments) intersect in the same point. • Point of concurrency: the point of intersection of the lines (or rays or segments)

  6. Theorem 5.5: Concurrency of Perpendicular Bisectors of a Triangle The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. PA = PB= PC Note: P is the Circumcenterof the Triangle

  7. Incenter of the triangle The point of concurrency of the angle bisectors and is always lies inside the triangle.

  8. Theorem 5.6: Concurrency of Angle Bisectors of a Triangle The angle bisectors of a triangle intersect at a point that is equidistant from the side of the triangle. PD = PE = PF

  9. What is an incenter? • What is a circumcenter? • What must occur for the segments from incenter to the sides of the triangle to be equidistant? Pt. of concurrency for angle bisector Pt. of concurrency for perpendicular bisector perpendicular

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