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Chapter 5
Thereoms and Vocab
12
Mathematics
9th Grade
12/10/2007

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Term
Perpendicular Bisector Thereom
Definition
If a point is on the perpendicular bisector of a segment, then it is quidistnat from the endpoints of the segment.
Term
Perpendicular Bisector Converse
Definition
If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.
Term
Angle Bisector Thereom  
Definition
If a point is on the bisector of an angle, then it is equidistant from the two siddes of the angle
Term
Angle Bisector Converse
Definition
If a point is in the interior of an angle and equidistant from the sides of an angle, then it lies on the bisector of the angle.
Term
Circumcenter
Definition
The lines containing the perpendicular bisectors of a triangle are concurrent. The circumcenter is equidistant from the vertices of the triangle.
Term
Incenter
Definition
The angle bisectors of a triangle are concurrent. The incenter is euidistant from the three sides of the triangle
Term
Centroid
Definition
The medians of a triangle are concurrent. The centroid is two-thirds of the distance from each vertex to the midpoint of the opposite side
Term
Orthocenter
Definition
The lines containing the altitudes of a triangle are concurrent.
Term
Midsegment Thereom
Definition
The segment connecting the midpoints if two sides of a triangle is parallel to the third side and is half its lenght
Term
Triangle Inequality
Definition
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Term
Hinge Thereom
Definition
If two sides of one triangle are concurrent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer thna the third side of the second.
Term
Converse of Hinge Thereom
Definition
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, then the included angle of the first is larger than the included angle of the second
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