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# geometry c

### postulates, theorems, definitions

TermDefinition
Theorem 1.1 if two distinct lines intersect, then they intersect at exactly one point
Theorem 1.2 if there is a line and a point not on the line, then there is exactly one plane that contains them
Theorem 1.3 if two distinct lines intersect, then they lie in exactly one plane
Theorem 1.4 each segment has exactly 1 midpoint
Theorem 1.5 midpoint theorem- if m is the midpoint of a segment of line AB, then: 2AM=AB and AM=1/2AB..... and 2MB=AB and MB=1/2AB
Theorem 1.6 in a half plane, through the end point of a ray lying in the edge of a half-plane, there is exactly one other ray such that the angle formed by the two rays has given measure between 0 and 180
Theorem 1.7 all right angles are congruent
Theorem 1.8 angle bisector theorem: if ray OX is the bisector of <AOB, then: 2m<AOX= m<AOB and m<AOX= 1/2m<AOB... and 2m<XOB= m<AOB and m<XOB= 1/2m<AOB
Theorem 1.9 if 2 angles are vertical, then they are congruent
Theorem 1.10 if 2 lines are perpendicular, then the pairs of adjacent angles they form are congruent
Theorem 1.11 if 2 lines intersect to form a pair of congruent adjacent angles, then the lines are perpendicular
Theorem 1.12 if there is given any point on a line in a plane, then there is exactly one line in that plane perpendicular to the given line at the given point
Theorem 1.13 if the exterior sides of 2 adjacent acute angles are perpendicular, then the angles are complementary
Theorem 1.14 if there is a point not on the line, then there is exactly one line perpendicular to the given line through the given point
Theorem 2.1 congruence of segments is reflexive, symmetric, and transtive
Theorem 2.2 congruence of angles is reflexive, symmetric, and transtive
Theorem 2.3 if 2 angles are supplements of congruent angles or of the same angles, then the 2 angles are congruent
Theorem 2.4 if 2 angles are complements of congruent angles
Theorem 3.1 if 2 parallel lines are intersected by a third plane, then the lines of intersection are parallel
Theorem 3.2 if parallel lines have a transversal, then alternate interior angles are congruent
Theorem 3.3 if parallel lines have a transversal, then alternate exterior angles are congruent
Theorem 3.4 if parallel lines have a transversal, then interior angles on the same side of the transversal are supplementary
Theorem 3.5 if a transversal intersecting 2 parallel lines is perpendicular to one of the lines, it is also perpendicular to the other line
Theorem 3.6
Created by: kiran_basra2