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segment addition postulate
 If point B falls between point A and C, and A, B, and C are collinear,
 then AB + BC = AC

2. Angle addition postulate
all the angles in a triangle add up to 180 degrees

3. Definition of parallel
two lines that don’t intersect and are coplanar

Definition of perpendicular
 two lines that intersect to
 form a right angle are perpendicular

what existst between any 2 points?
a line

through any 3 noncolinear points there exists what?
a plane

Addition Prop of Equality
a = b, then a + c = b + c

waht is RAT
right angle congruency all right angles are congruent

Congruent Supplements Theorem
 if two angles are supplementary to the same angle (or to congruent
 angles) then they are congruent

Congruent Complements Theorem
 if two angles are complementary to the same angle (or to congruent
 angles) then they are congruent

Linear Pair Postulate (LPP
 if two angles form a linear
 pair, then they are supplementary

Parallel postulate
 if there is a line and a point not on that line, then there is exactly
 one line through the point parallel to the given line

Perpendicular Postulate
 if there is a line and a
 point not on the line, then there is exactly one line through the point
 perpendicular to the given line

Corresponding angles postulate
 if two lines cut by a transversal are parallel, then the corresponding
 angles are congruent

Transitive property of parallel lines
 if two coplanar lines are parallel to the same line, then they are
 parallel to each other

Slopes of parallel lines postulate
 in a coordinate plane, two nonvertical lines are parallel if and only
 if they have the same slope

Slopes of perpendicular lines postulate
 in a coordinate plane, two
 nonvertical lines are perpendicular if and only if they have slopes that are
 negative reciprocals

If two lines intersect to form a linear pair of congruent angles, then
the lines are perpendicular (theorem)
 If two lines intersect to form a linear pair of congruent angles, then
 the lines are perpendicular (theorem)

what postulates prove congruency?
 sss
 aaa
 sas
 asa
 hl

what is cpctc
(corresponding parts of corresponding triangles are congruent)

base angles theorem
 if two sides of a triangle are congruent, then the angles opposite these
 sides are also congruent

base angles theorem corollary
if a triangle is equilateral, then it is equiangular

converse of the base angles theorem
 if two angles in a triangle
 are congruent, then the two opposite sides are congruent

corollary to the converse of the base angles theorem
if a triangle is equiangular, then it is equilateral

Corresponding lengths in similar polygons
 if two polygons are
 similar, then the ratio of any two lengths in the polygon is equal to the scale
 factor.

Perimeters of similar triangles
 if two polygons are
 similar, then the ratio of their perimeters is equal to the ratio of the
 lengths of their corresponding sides (scale factor)

waht postulates prove similarity?
 aa if two angles of one triangle are congruent to two angles of another
 triangle, then the triangles are similar
 sss
 sas

Triangle Proportionality Theorem
 if a line parallel to one
 side of a triangle intersects the other two sides then it divides the two sides
 proportionally

converse of the Triangle Proportionality Theorem
 if a line intersects 2 sides of a triangle and it divides the sides
 proportionally, then it is parallel to the other side

Midsegment Theorem
 the midsegment of a triangle is half the length of the side it does
 not intersect and parallel to that side

