1. Warm Up

2. HW Check

3. HW Check Midsegment worksheet
TR 2. AC
10. 33, 66
11. D(1,3), E(7,3).
Length of DE = 6, Length of AC = 12
Slope of DE = 0, Slope of AC = 0 therefore ll lines

4. 5-3 Points of Concurrency
When three or more lines meet at the same point, they are called concurrent.
NOT CONCURRENT!

5. Perpendicular Bisectors of Triangles
The Perpendicular Bisectors of the sides of a triangle are concurrent at the circumcenter which is equidistant from all vertices of the triangle.

6. Points of Concurrency Perpendicular Bisectors Angle Bisectors
There are four special “Points of Concurrency” (points where three lines meet) in triangles.
They are created by the following types of lines:
Perpendicular Bisectors
Angle Bisectors
Altitudes
Medians

7. Draw lines from B to verticies

8. Angle Bisectors of a Triangle
The angle bisectors of the angles of a triangle are concurrent at the incenter, which is equidistant from the sides of the triangle

9. Draw perp dist to sides, same

10. Altitude of a Triangle
An altitude of a triangle is the segment that extends from a vertex of a triangle perpendicular to the opposite side.
The altitudes of a triangle are concurrent at a point called the orthocenter.

12. Median of a Triangle
The median of a triangle is a segment that connects a vertex to the midpoint of the opposite side.
The medians of a triangle are concurrent at the Centroid, which is two-thirds the distance from each vertex to the midpoint of the opposite side.

14. Example 1 Angle Bisector Perpendicular Bisector Altitude Median
Name the following:
Angle Bisector
Perpendicular Bisector
Altitude
Median
A.B. = BE
P.B. = FG
Alt = HB
M = DA

15. Example 2
Find the Circumcenter

16. Helpful Equations for Centroid Problems
Median = Shorter side + Longer side
Shorter Side =
Longer Side =
Smaller Side =
Find the circumcenter of a triangle given coord plane (5-7 of hw), name each line, centroid problems, name concurrent point of lines

17. Classwork
Equations: Smaller side + bigger side = whole thing, Smaller side = 1/3 * median, longer side = 2/3 * median, 2*smaller = longer side

18. Hint: sketch triangle.

19. Homework
Worksheet – On # 5-7, find the circumcenter