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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
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2. Angle addition postulate
all the angles in a triangle add up to 180 degrees
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3. Definition of parallel
two lines that don’t intersect and are coplanar
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Definition of perpendicular
- two lines that intersect to
- form a right angle are perpendicular
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what existst between any 2 points?
a line
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through any 3 noncolinear points there exists what?
a plane
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Addition Prop of Equality
a = b, then a + c = b + c
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waht is RAT
right angle congruency all right angles are congruent
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Congruent Supplements Theorem
- if two angles are supplementary to the same angle (or to congruent
- angles) then they are congruent
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Congruent Complements Theorem
- if two angles are complementary to the same angle (or to congruent
- angles) then they are congruent
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Linear Pair Postulate (LPP
- if two angles form a linear
- pair, then they are supplementary
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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
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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
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Corresponding angles postulate
- if two lines cut by a transversal are parallel, then the corresponding
- angles are congruent
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Transitive property of parallel lines
- if two coplanar lines are parallel to the same line, then they are
- parallel to each other
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Slopes of parallel lines postulate
- in a coordinate plane, two non-vertical lines are parallel if and only
- if they have the same slope
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Slopes of perpendicular lines postulate
- in a coordinate plane, two
- non-vertical lines are perpendicular if and only if they have slopes that are
- negative reciprocals
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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)
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what postulates prove congruency?
- sss
- aaa
- sas
- asa
- hl
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what is cpctc
(corresponding parts of corresponding triangles are congruent)
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base angles theorem
- if two sides of a triangle are congruent, then the angles opposite these
- sides are also congruent
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base angles theorem corollary
if a triangle is equilateral, then it is equiangular
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converse of the base angles theorem
- if two angles in a triangle
- are congruent, then the two opposite sides are congruent
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corollary to the converse of the base angles theorem
if a triangle is equiangular, then it is equilateral
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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.
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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)
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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
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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
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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
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Midsegment Theorem
- the midsegment of a triangle is half the length of the side it does
- not intersect and parallel to that side
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