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?

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Presentation transcript:

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?

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

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 _____________________.

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

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 ______________

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)?

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)?

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)?

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

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

Problem: Identifying and Using the Incenter of a Triangle GE = 2x – 7 and GF = x + 4. What is GD?

Problem: Identifying and Using the Incenter of a Triangle QN = 5x + 36 and QM = 2x + 51. What is QO?

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

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

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

Homework: Page 305, #7-10 all, 14-19 all