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Geometry 6th

Postulates and Theorems

TermDefinition
Angle Bisector Bisects an angle (cuts in half). Any point in the angle bisector is equidistant from the sides of the angle.
Perpendicular Bisector does not have to start at a vertex. When it Intersects the opposite side it makes a right angle (perpendicular) and bisects it.
Altitude Does not have to start at a vertex. When it intersects the opposite side it makes a right angle.
Median Does have to start at a vertex. When it intersects the opposite it bisects it.
Midsegment Connects two midpoints of 2 sides of a triangle. The length of the midsegment is half the 3rd side and it is parallel to the 3rd side.
Thm. 5.2 Perpendicular Bisector Theorem In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Thm. 5.5 Angle Bisector Theorem If a point is on the bisector of an angle, the it is equidistant from the two sides of the angle.
Thm. 5.10 Side to Angle Theorem If one side of a triangle is longer than another side than the angle opposite the longer side is larger than the angle opposite the shorter side.
Thm. 5.11 Angle to Side Theorem If one angle is larger than another angle the side opposite the larger angle is longer than the side opposite the smaller angle.
Thm. 5.12 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Thm. 5.13 Hinge Theroem If 2 sides of one triangle are congruent to 2 sides of another triangle,and the included angle of the 1st triangle is larger 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.
Thm. 5.14 Converse of Hinge Theorem If 2 sides of one triangle are congruent to 2 sides of another triangle, and the 3rd side of the 1st is longer than the 3rd side of the 2nd, then the included angle of the 1st is larger than the included angle of the 2nd.
Created by: daviddunham