1. Homework Quiz

2. Warmup

3. Need Graph Paper/Compass

4. 5.3 Concurrent Lines, Medians, and Altitudes

5. Learning Target I can tell the difference between a median, altitude, perpendicular bisector and angle bisector of a triangle.

6. When three or more lines intersect at one point, they are concurrent. The point at which they intersect is called the point of concurrency.

7. Circumcenter of a Triangle: The point of concurrency of the perpendicular bisectors of a triangle. The points of a triangle are equidistant from the circumcenter The circumcenter of a triangle is also the center of the circle circumscribed about the triangle.

10. Lets Practice Please write the following problems down

11. Do #1-3

12. Do #11-13 Find the circumcenter only

13. Incenter of a Triangle: The point of concurrency of the angle bisectors of a triangle. Here the circle is inscribed in the triangle

15. Name the point which represents the incenter

16. Median of a Triangle: A segment whose endpoints are a vertex and the midpoint of the opposite side. EX

18. Centroid: the point of concurrency of the medians. Note…its also called the center of gravity of a triangle because it is the point where the triangle will balance.

20. Something to know… The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. EX:

22. Altitude of a triangle: the perpendicular segment from a vertex to the line containing the opposite side.

24. In an acute triangle, the altitude is inside the triangle. In a Right triangle the altitude is a side. In an obtuse triangle, an altitude will be outside of the triangle.

25. Orthocenter of a Triangle: Point of concurrency for altitudes of a triangle.

26. Lets do 11-13 on the worksheet

27. Constructions -Incenter -Circumcenter

28. RECAP ( A lot to keep track of here): Perpendicular Bisectors  Circumcenter Angle Bisectors  Incenter Medians  Centroid Altitudes  Orthocenter

29. On the worksheet, do #5-10

30. Review 5.1 p.246 #2-18 even, #22-25, #29-31 (tougher)

31. Review 5.2: p.251 #1-25 (skip 5, 11, 16, 17)

32. Review 5.3 p. 259-261 #2-22, 27-28

33. QUIZ Tomorrow on 5.1-5.3