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Transcript
Advanced Geometry Topic 5 – Relationships within Triangles NOTES – Bisectors in Triangles (5-4) Name: _____________________________________________________ Date: _________________________________ Period: ____________ Vocabulary Concurrent – when 3 or more lines intersect at one point, they are concurrent Point of concurrency – the point at which line intersect Circumcenter of a triangle – the point of concurrency of the perpendicular bisectors of a triangle Incenter of a triangle – the point of concurrency of the angle bisectors of a triangle Theorem 5-6 – Concurrency of Perpendicular Bisectors Theorem Theorem Diagram Symbols The ____________________ ____________________ of the sides of a triangle are ____________________ at a point ____________________ from the vertices. Theorem 5-3 – Concurrency of Angle Bisectors Theorem Theorem Diagram Symbols The ____________________ of the angles of a triangle are ____________________ at a point ____________________ from the sides of the triangle. 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)? (from the textbook) Using a Circumcenter A town planner wants to locate a new fire station equidistant from the elementary, middle, and high schools. Where should he locate the station? Using a Circumcenter In Problem 3 above, the town planner wants to place a bench equidistant from the three trees in the park. Where should he place the bench? Identifying & Using the Incenter of a Triangle a. 𝑄𝑁 = 5𝑥 + 36 and 𝑄𝑀 = 2𝑥 + 51. What is QO ? b. Is it possible for QP to equal 50? Explain.