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Postulate one

equal quantities plus equal quantities are equal

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postulate two

any given quantity equals itself

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postulate three

equal quantities minus equal quantities are equal

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theorem one

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

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postulate four

construct line segement

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postulate five

construct circle

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theorem two

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

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theorem three

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

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theorem four

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

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theorem five

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

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theorem seven

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

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theorem seven

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

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postulate nine

equal quantities multiplied or divided by equal quantities are equal

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postulate ten

with a straightedge, any given line segment can be extended

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postulate eleven

substitution

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theorem nine

if perpendicular then ninety degrees

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theorem ten

if ninety degrees then perpendicular

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theorem eleven

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

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theorem eight

vertical angles are equal

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postulate eight

any whole quantity equals the sum of its parts

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postulate thirteen

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

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theorem twelve

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

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theorem thirteen

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

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theorem fourteen

if two lines are parallel then he corresponding angles are equal

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