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Apply properties of perpendicular bisectors and angle bisectors of a triangle.

Objectives. Apply properties of perpendicular bisectors and angle bisectors of a triangle. The circumcenter can be inside the triangle, outside the triangle, or on the triangle.

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Apply properties of perpendicular bisectors and angle bisectors of a triangle.

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  1. Objectives Apply properties of perpendicular bisectors and angle bisectors of a triangle.

  2. The circumcenter can be inside the triangle, outside the triangle, or on the triangle.

  3. __________ - A circle in a polygon that intersects each line that contains a side of the polygon at exactly one point. _________ - A circle that contains all the vertices of a polygon The incenter is the center of the triangle’s inscribed circle. The circumcenter of ΔABC is the center of its circumscribed circle.

  4. Check It Out! Example 1a Use the diagram. Find GM.

  5. Check It Out! Example 1b Use the diagram. Find GK.

  6. Check It Out! Example 1c Use the diagram. Find JZ.

  7. Remember! The distance between a point and a line is the length of the perpendicular segment from the point to the line.

  8. Unlike the circumcenter, the incenter is always inside the triangle.

  9. MP and LP are angle bisectors of ∆LMN. Find the distance from P to MN. Example 3A: Using Properties of Angle Bisectors

  10. Example 3B: Using Properties of Angle Bisectors MP and LP are angle bisectors of ∆LMN. Find mPMN.

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