Geometry Relationsships of Triangles

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  1. What is a midsegment of a triangle and what do you know about it?
    A midsegment of a traingle is a segment that has the midpoints of a triangle's sides as endpoints. The midsegment is paralel to the side it does not touch, and is half of its length. It also makes two similar triangles
  2. What is a perpendicular bisector?
    A line that goes through the midpoint of a line and is perpendicular to the line. The points on the line are equidistant from the endpoints.
  3. What is a point of concurrency?
    It is the point where three or more lines intersect at the same point.
  4. What do you know about perpendicular bisectors of a triangle?
    The point of concurrency is called a circumcenter. The circumcenter is the point that is equidistant to all of the certices of a triangle. The perpendicular bisectors themselves however, are NOT congruent.
  5. What is a circumcenter?
    It is the point of concurrency of the perpendicular bisectors of a triangle. It is the center of the circle that goes around the triangle. If the triangles is acute, it is inside the circle. It it is a right triangle it is on the hypotnuse. If it is obtuse, then it is outside of the circle.
  6. What do you know about angle bisctors?
    It is the angle that bisects one of the angles in a trianlge. Its point of concurrency is called the incenter. The points on an angle bisector are equidistant from the sides of the traingle.
  7. What is the incenter?
    The point of concurrency of angle bisectors of a triangle. They are the center of the circle that is inside of the triangle and touches each side at one point. The incenter is also equidistant from all sides of the triangle.
  8. What do you know about medians of a traingle?
    A medians are line segments in a triangle drawn from the midpoint of a side to the opposite vertex. The intersect at the centroid. *The distance from the centroid to the vertex is twice as long as the distance from the centroid to the midpoint*.
  9. What is a centroid?
    A centroid is the point of concurrency of the medians of a triangle?
  10. What do you know about the altitudes of a triangle?
    The altitude is the line segment from the vertex of one side to the line across from, in wich the line created is perpendicular to the line across from it. Its point of concurrency is called the orthocenter.
  11. What is the orthocenter of a traingle?
    The point of concurrency of the altitiudes of a triangle.
  12. What do you know about the sides of the triangle and the angles opposite them?
    If you know that one of the angles is the largest, then the side across from it is also the biggest, and vice versa. If it is in the middle, then so is the side. If the side is the smallest, so is the angle.
  13. What about the lengths of the sides of a triangle have to be?
    The two shorter sides bust be GREATER THAN the largest side.
  14. What is the hinge theorem?
    If two sides that correspond in traingles are congruent, then the trianlge with the largest angle between them has the largest side.
  15. What must you do on an indirect proof?
    Assume that the false thing is true, and then use a contradicting statement to prove your answer.
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Geometry Relationsships of Triangles
Review of Relationships of Triangles for the Geometry Regents exam. Have paper to draw and take notes on things that oyu forgot!
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