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Postulate one

equal quantities plus equal quantities are equal

postulate two

any given quantity equals itself

postulate three

equal quantities minus equal quantities are equal

theorem one

if one quantity equals a second and the second equals a third, then the first equals the third

postulate four

construct line segement

postulate five

construct circle

theorem two

if a line segment is given, then another line segment can be constructed equal to it

postulate six

sss

postulate seven

sas

theorem three

if a line segment is given, then its midpoint can be determined

theorem four

if an angle is given, the an angle can be constructed equal to it

theorem five

if an angle is given, then its bisector can be constructed

theorem seven

if a triangle has two sides equal, then the angles opposite these sides are equal

theorem seven

if a point is not on a line segment, then a perpendicular from the point to the line segment can be constructed

postulate nine

equal quantities multiplied or divided by equal quantities are equal

postulate ten

with a straightedge, any given line segment can be extended

postulate eleven

substitution

theorem nine

if perpendicular then ninety degrees

theorem ten

if ninety degrees then perpendicular

postulate twelve

asa

theorem eleven

if a transversal forms equal alt. interior angles with two line segments, then the line segments form parallels

theorem eight

vertical angles are equal

postulate eight

any whole quantity equals the sum of its parts

postulate thirteen

there is exactly one parallel to a given line through a point that is not on the line

theorem twelve

if two lines are parallel then the alt. interior angles are equal

theorem thirteen

if a transversal form equal corresponding angles with two line segments, then the line segments are parallel

theorem fourteen

if two lines are parallel then he corresponding angles are equal