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Geometry

Postulates and Theorems

TermDefinition
Angle Bisecter bisects an angle (cuts in half). any point on the angle bisecter is equadistance from the side of the angle.
Perpendicular Bisecter 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 have to start at a vertex. when intersects, makes right angle
Median starts at vertex. when intersectes, makes right angle
Mid-Segment connects two midpoints of two sides of a triangle. length is half of 3rd side, and is parallel
Thm. 5.2 Perpendicular Bisecter Theorem in a plane, if a point is on the perpendiclar bisecter of a segment, then it is equadistant from the endpoints of the segment
Thm. 5.5 Angle Bisecter Theorem if a point is on the bisecter of an angle, then it is equadistant from the 2 sides of the angle
Thm. 5.10 Side to Angle Theorem if one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite of the shorter side
Thm. 5.11 Angle to Side Theorem if one angle is larger than another, then 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 legths of any two sides of a triangle is greater than the length of the third side
Thm. 5.13 Hinge Thm. If 2 sides of 1 tri. are congruent to 2 sides of another tri, and the included angle of the 1st tri. is larger than the included angle of the 2nd tri, then the 3rd side of the 1st tri is longer than the 3rd side of the 2nd tri
Thm. 5.14 Converse of the Hinge Thm. If 2 sides of 1 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: laurengrawunder