Geometry Elliott
Terms
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- circumcenter
- intersection of the triangles 3 perpendicular bisectors
- incenter
- intersection of the triangles 3 angle bisectors
- centroid
- intersection of the triangles 3 medians
- orthocenter
- intersection of the triangles 3 altitudes
- altitude
- segment from the vertex of a triangle and perpendicular to a line containing the opposite side
- median
- segment from the vertex of a triangle tot he midpoint of the opposite side
- angle bisector
- ray that divides an angle into two adjacent angles that are congruent; all points on an angle bisector are equidistant from the angles 2 rays
- perpendicular bisector
- intersects a side at its midpoint and forms a right angle with the side
- perpendicular bisector theorem
- If a point is on the perpendicular bisector of a segment, then its equidistant from the endpoints of the segment.
- 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.
- angle bisector theorem
- If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
- converse of the angle bisector theorem
- If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.
- concurrent lines
- 3 or more lines intsersect in the same point
- point of concurrency
- point of intersection of the concurrent lines
- midsegment
- segment that connects the midpoints of 2 sides of a triangle
- midsegment theorem
- The segment connecting the midpoints of 2 sides of a triangle is parallel to the 3rd side and is half as long/
- Exterior Angle Inequality
- The measure of an exterior angle of a triangle is greater than the measure of either of the 2 nonadjacent interior angles.
- Triangle Inequality Theorem
- The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.
- Hinge Theorem
- If 2 sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the 1st triangle is greater than the included angle of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle.
- Converse of the Hinge Theorem
- If 2 sides of 1 triangle are congruent to 2 sides of another triangle and the 3rd side of the 1st triangle is longer then the 3rd side of the 2nd triangle, then the included angle of the 1st triangle is greater than the included angle of the 2nd triangle.