5.2: Circumcenters and Incenters

1. 5.2: Circumcenters and Incenters Objectives: To know and apply the properties of circumcenters. To know and apply the properties of incenters.

2. Vocabulary:

3. 5.2: Circumcenters and Incenters Activity: Need: 2 pieces of patty paper. A pencil or felt tip pen (2 colors preferably) A strait-edge (ruler) Glue stick to share with a partner On your patty paper:  Draw an isosceles triangle on each paper  Draw an acute triangle on each paper  Draw a right triangle on each paper  Draw an obtuse triangle on each paper

4. 5.2: Circumcenters and Incenters Activity: Label each paper:  bisector  bisector

5. Perpendicular Bisectors of a triangle… • bisect each side at a right angle • meet at a point called the circumcenter • The circumcenter is equidistant from the 3 vertices of the triangle. • The circumcenter is the center of the circle that is circumscribed about the triangle. • The circumcenter could be located inside, outside, or ON the triangle. C

6. Using the Circumcenter…. Example 1 Find all measures that are possible in the figure.

7. Example 2: Finding the Circumcenter of a Right Triangle Find the circumcenter of ∆HJK with vertices H(0, 0), J(10, 0), and K(0, 6). Step 1 Graph the triangle. Step 2 Draw in two perpendicular bisectors. Step 3 Find the intersection of the 2 lines. Answer: the circumcenter is at (5, 3)! Now complete: page 311 #12 – 17, 20 (10 minutes!)

8. Now complete: page 311 #12 – 17, 20

9. Paste-able! Angle Bisectors of a triangle… • bisect each angle • meet at the incenter • The incenter is equidistant from the 3 sides of the triangle. • The incenter is the center of the circle that is inscribed in the triangle. • The incenter is always inside the circle. I

10. QX and RX are angle bisectors of ΔPQR. Find the distance from X to PQ. Example 1 Find mPQX.

11. 2.JP, KP, and HP are angle bisectors of ∆HJK. Find the distance from P to HK. Example 2

12. Now complete: page 311 #12 – 32