math final

• equidistant 


  point is the same distance from two figures
• Perpendicular Bisector Theorem 


  In a plane, if a point lands on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment
• Converse of the Perpendicular Bisector Theorem

  In a plane, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment
• Angle Bisector Theorem


  If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle (DS = DC)
• Converse of the Angle Bisector Theorem

  If a point is in the interior of an angle and is equivalent from the two sides of the angle, then it lies on the bisector of the angle
• Median


  A segment from a vertex to the midpoint of the opposite side
• The three medians of a triangle meet at the centroid
• centroid


  intersection of all the medians
• centroid theorem


  The centroid of a triangle is 2/3s of the distance from each vertex to the midpoint of the opposite side
• Centroid Formula = (x, y) = (x1+x2+x3/3, y1+y2+y3/3)
• triangle midsegment


  a segment that connects the midpoint of two sides of the triangle
• Triangle Midsegment Theorem

  The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side
• Triangle Larger Angle Theorem


  If one side of a triangle is larger than another side, then the angle opposite the larger side is larger than the angle opposite the shorter side
• Triangle Longer Side Theorem


  If one angle of a triangle is longer than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
• Triangle Inequality Theorem

  The sum of the lengths of any two sides of a triangle is greater than the length of the third angle
• When two sides of a triangle stay the same length and the third side changes length, it is called a hinge effect. If the included angle of the two sides gets bigger, then the third side gets bigger
• Hinge Theorem


  If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger then the included angle of the second, then the third side of the first is longer then the third side of the second
• Converse of the Hinge Theorem


  If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, than the included angle of the first is larger than the included angle of the second