1. WARM UP:
What is RU?
In the diagram above, if RT is extended to contain a point W so the UW has a length of 8, what is the length of SW?
What is CD?

2. 5.3 - Bisectors in Triangles
I can identify properties of perpendicular bisectors and angle bisectors.

3. When three or more lines intersect at one point, they are __________
When three or more lines intersect at one point, they are __________. The point at which they intersect is the _____________________.

4. Concurrency of Perpendicular Bisectors Theorem
Diagram
Symbols
The _____________________________ of a triangle are ____________ at a point equidistant from the vertices.

5. Huh???
The ________________ is the point where the three perpendicular bisectors of a triangle meet.
In the special case of a ______________, the circumcenter lies exactly at the __________ of the
______________

6. Problem: Finding the Circumcenter of a Triangle
What are the coordinates of the circumcenter of a triangle with vertices P(0, 6), O(0, 0), and S(4, 0)?

7. Problem: Finding the Circumcenter of a Triangle
What are the coordinates of the circumcenter of the triangle with vertices A(2, 7), B(10, 7), and C(10, 3)?

8. Problem: Finding the Circumcenter of a Triangle
What is the center of the circle that you can circumscribe about a triangle with vertices A(0, 4), B(0, 0), and C(8, 0)?

9. Concurrency of Angle Bisectors Theorem
Diagram
Symbols
The ___________________________________________________are concurrent at a point ____________from the sides of the triangle.

10. Huh??
The ______________ is the point where the three angle bisectors of a triangle meet.

11. Problem: Identifying and Using the Incenter of a Triangle
GE = 2x – 7 and GF = x What is GD?

12. Problem: Identifying and Using the Incenter of a Triangle
QN = 5x + 36 and QM = 2x What is QO?

13. Problem: Identifying and Using the Incenter of a Triangle
GB = 8x – 7 and GD = 5x What is GF?

14. After: Lesson Check
1. What are the coordinates of the circumcenter of the following triangle?

15. After: Lesson Check
2. In the figure below, TV = 3x – 12 and TU = 5x – 24. What is the value of x?

16. Homework:
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