1. Unit Essential Question: How do you use the properties of triangles to classify and draw conclusions?

2. Essential Question: What are the different classifications of triangles?

3. Classifying Triangles

4. Example:

5. Midsegment A midsegment joins the midpoints of two sides of a triangle.

6. Finding Lengths

9. Perpendicular Bisector Draw a line that is Perpendicular to this segment and bisects the segment: The perpendicular bisector of a segment is a line perpendicular to a segment at its midpoint.

10. Essential Question: What are the attributes of bisectors?

11. Perpendicular Bisector Theorem

12. DC Find the set of points equidistant from the White House and the Jefferson Memorial:

14. Distance from a point to a line: How far is it from this point to the line? How should we measure the distance?

15. Angle Bisector Theorem

16. Find FD.

17. Angle Bisector Theorem

19. Essential Question: Can you identify the median, altitude, angle bisector, and perpendicular bisector of a triangle?

20. Concurrency When three or more lines intersect at a common point, they are concurrent. The point of intersection of concurrent lines is the point of concurrency.

21. Concurrency in Triangles

22. Circumcenter & Incenter Point of concurrency of Perpendicular Bisectors forms the circumcenter, which is used to circumscribe a triangle. Point of concurrency of Angle Bisectors form the incenter, which is used to inscribe a triangle.

23. Median Will the medians be concurrent? Yes, at the centroid.

24. Altitude The altitude of a triangle is the perpendicular segment from a vertex to the line containing the opposite side. (Also called the height).

25. Are the Altitudes Concurrent? The point of concurrency is called the orthocenter.

26. Which special segments are pictured?

27. Practice

28. Essential Question: What is the relationship between the sides and opposite angles in a triangle?

29. What does this mean? Can we prove it?

32. Converse of Opposite Parts Theorem

33. Opposite Parts Theorem

34. List the Sides from Shortest to Longest

35. Triangle Inequality Theorem What is the special relationship?

36. Essential Question: How do you use the triangle inequality theorem to determine a range for the third side of a triangle?

37. Triangle Inequality Theorem

38. Can you make a triangle?

39. Range of Possible Lengths a – b < x < a + b