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Special segments of a triangle, points of intersection, inequalities of triangle

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Vocab word
Definition
Angle bisector   splits an angle into congruent parts  
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Perpendicular bisector   splits a segment at its midpoint perpendicularly  
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Median   a segment that connects a vertex of a triangle to the midpoint of the opposite side  
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Altitude   a segment of a triangle that goes from a vertex perpendicularly to the opposite side  
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Midsegment   a segment in a triangle that connects two midpoints  
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Midpoint   a point in the middle of a segment that cuts it into two congruent parts  
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Orthocenter   the point of intersection of the altitudes  
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Circumcenter   the point of intersection of the perpendicular bisector  
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Incenter   the point of intersection of the angle bisectors  
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Centroid   the point of intersection of the medians  
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Center of inscribed circle   Incenter  
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Center of circumscribed circle   Circumcenter  
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2/3 the distance from vertex to midpoint   Centroid  
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Equidistant from the sides of a triangle   Incenter  
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Equidistant from the vertices of the triangle   Circumcenter  
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Triangle Inequality Theorem   Two sides of a triangle must add up to be bigger than the third side  
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Largest side of a triangle   Opposite the largest angle  
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Smallest side of a triangle   Opposite the smalled angle  
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Largest angle of a triangle   Opposite the largest side  
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Smallest angle of a triangle   Opposite the smallest side  
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Hinge Theorem   If 2 sides of 2 triangles are congruent and the included angle of the first is bigger, then the third side of the first is bigger  
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Hinge Theorem Converse   If 2 sides of 2 triangles are congruent and the third side of the first is bigger, then the included angle of the first is bigger  
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Direct Proof   Using properties, definitions, postulates and theorems to prove something directly  
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Indirect Proof   Temporarily assuming the opposite of what you are trying to prove to reach a contradiction  
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Created by: jenkroesen
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