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Triangle Segments

Learn about the midsegments, perpendicular bisectors, angle bisectors, medians, altitudes, circumcenter, incenter, centroid, and orthocenter of a triangle.

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Triangle Segments

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  1. Triangle Segments

  2. Triangle Midsegment A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. Example: DE ____

  3. Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half (1/2) as long. __ If DE is a midsegment of △ABC, then DE II AC and DE = ½ AC or AC = 2(DE) __ __ __ __ __ __ IIis the symbol for parallel

  4. Perpendicular Bisector A line, segment, or ray that divides a segment into two equal parts and is perpendicularto the segment. ⊥= symbol for perpendicular Perpendicular = a straight line at an angle of 90° to a given line, plane, or surface.

  5. Perpendicular Bisector Theorem If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. ____ ____ ____ ____ ____ ____ < > If CD ⊥ AB and AD ≅ DB then AC ≅ CB

  6. Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. ____ ____ ____ ____ ____ ____ < > If AC ≅ CB and CD ⊥ AB then AD ≅ DB

  7. Circumcenter The point at which the three perpendicular bisectors intersect in a triangle.

  8. Angle Bisector Angle Bisector Theorem – If a point is on a bisector of an angle, then the point is equidistance from the sides of the angle. Converse of the Angle Bisector Theorem – If a point is on the interior of an angle and equidistant from the sides of the angle, then the point is on the angle bisector. A line, segment, or ray that divides an angle into two equal parts.

  9. Incenter The point at which the three angle bisectors intersect in a triangle.

  10. Parts of a Right Triangle Side C is called the Hypotenuse. Sides A and B are called Legs.

  11. Median Vertex – A point where two or more line segments meet. A segment that connects a vertex of a triangle to the midpoint of the opposite side.

  12. Centroid The point at which the three medians intersect in a triangle.

  13. Altitude Altitudes can be found inside a triangle, outside a triangle, or a side of a triangle. A segment joining a vertex of a triangle to the opposite side so that it is perpendicular to that side.

  14. Orthocenter All three altitudesof a triangle intersect at a point called the orthocenter.

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