## Proofs: Postulates

##### Created by:

cynthia_yue  on April 16, 2012

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# Proofs: Postulates

 Line PostulateYou can construct exactly one line through any two points. In other words, two points determine a line.
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Line Postulate You can construct exactly one line through any two points. In other words, two points determine a line.
Line Intersection Postulate The intersection of two distinct lines is exactly one point.
Segment Duplication Postulate You can construct a segment congruent to another segment.
Angle Duplication Postulate You can construct exactly one angle bisector in any angle
Parallel Postulate Through a point not on a given line, you can construct exactly one line parallel to the given line.
Perpendicular Postulate Through a point not on a given line, you can construct exactly one line perpendicular to the given line.
Segment Addition Postulate If point B is on line segment AC and between points A and C, then AB + BC = AC.
Angle Addition Postulate If point D lies in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC.
Linear Pair Postulate If two angles are a linear pair, then they are supplementary.
Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the corresponding angles are congruent. Conversely, if two lines are cut by a transversal forming congruent corresponding angles, then the lines are parallel.
SSS Congruence Postulate If the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
SAS Congruence Postulate If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.
ASA Congruence Postulate If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.

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