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Understanding Points of Concurrency in Geometry

Explore the properties of perpendicular bisectors and angle bisectors in geometry. Learn about points of concurrency, including the circumcenter and incenter of a triangle. Discover how these points relate to the triangle's vertices and sides, and where they lie in relation to the triangle. Practice finding the circumcenter and incenter to enhance your understanding of geometric concepts.

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Understanding Points of Concurrency in Geometry

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  1. 5-3Points of Concurrency Objective: To identify properties of perpendicular bisectors and angle bisectors

  2. Concurrent: When three or more lines, segments, rays or planes have a point in common. Point of Concurrency: The point of intersection. Point of Concurrency Concurrent Not Concurrent

  3. The three perpendicular bisectors of a triangle are concurrent. Point of concurrency is called circumcenter. The circumcenter of a triangle is equidistant from the vertices and is the center of the circle.

  4. The circumcenter of a triangle can be inside, on , or outside a triangle.

  5. Finding the Circumcenter of a triangle.

  6. The point of concurrency of the angle bisectors of a triangle is called the incenterof the triangle. p. 305: 7, 8, 9, 15, 17, 37, 38 The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle. P is the center of the circle that is inscribed in the triangle.

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