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Brain Strain Find the value of x. x x x xx

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Special Segments in Triangles

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MedianMedian

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Altitude Altitude

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Tell whether each red segment is an altitude of the triangle. The altitude is the true height of the triangle.

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Perpendicular Bisector

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Tell whether each red segment is an perpendicular bisector of the triangle.

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Angle Bisector

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Drill & Practice Indicate which special triangle segment the red line is based on the picture and markings

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Points of Concurrency

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The intersection of the angle bisectors is called the INCENTER. Equidistant to the sides

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The intersection of the altitudes is called the ORTHOCENTER.

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The intersection of the medians is called the CENTROID. Vertex to Centroid is Twice as Long as Centroid to Midpoint

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The intersection of the perpendicular bisector is called the CIRCUMCENTER. Equidistant to the vertices

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Memorize these! MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter Angle Bisectors/Incenter Perpendicular Bisectors/Circumcenter

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Will this work? MC AO ABI PBCC My Cat Ate Our Apples But I Prefer Blue Cheese Crumbles

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Special Property of Medians

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Theorem Vertex to CENTROID is TWICE as long as CENTROID to MIDPOINT vertex centroid midpoint

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A B F X E C D

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A B F X E C D

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In ABC, AN, BP, and CM are medians. A B M P E C N If EM = 3, find EC. Ex: 1

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In ABC, AN, BP, and CM are medians. A B M P E C N If EN = 12, find AN. Ex: 2

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In ABC, AN, BP, and CM are medians. A B M P E C N If CM = 3x + 6, and CE = x + 12, what is x? CM = CE + EM Ex: 3

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Special Segments in a Triangle (pick a triangle, any triangle)

Special Segments in a Triangle (pick a triangle, any triangle)

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