Math Theorems & Postulates

vociyeme's version from 2017-10-14 13:37

Triangles, Segments, and Properties

Segment Addition PostulateIf 3 points A B and C are collinear and B is between A and C, the AB + BC = AC
Angle Addition PostulateIf point B is in the interior of angle AOC, then angle AOB + BOC = AOC and if AOC is a straight angle, then AOB + BOC = 180.
Reflexive PropertyIf line AB is congruent to line AB then angle A is congruent to angle A
Symmetric PropertyIf line AB is congruent to line CD then line CD is congruent to line AB
Transitive PropertyIf line AB is congruent to CD and CD is congruent to EF then line AB is congruent to line EF
Vertical Angles TheoremVertical angles are congruent.
Congruent Supplements TheoremIf two angles are supplements of congruent angles, then two angles are congruent
Congruent Complements TheoremIf two angles are complements of congruent angels, then the 2 angles are congruent

Points of a Triangle

Bisector Theorems

Triangle Midsegment TheoremIf a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length
Triangle Inequality TheoremThe sum of the lengths of any two sides of a triangle is greater than the length of the third side
Perpendicular Bisector TheoremIf a point is on the perpendicular bisector of a segment, then it is equidistant from the enpoints of the segment
Converse of Perpendicular Bisector TheoremIf a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
Angle Bisector TheoremIf a point is on the angle bisector of an angle, then it is equidistant from the sides of the angle
Converse of Angle Bisector TheoremIf a point is equidistant from the sides of an angle, then it is on the angle bisector.
Hinge Theorm*If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is greater than the included angle of the second triangle, then the third side of the first triangle is greater than the third side of the second triangle.