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27 terms

Geometry Postulates and Theorems

STUDY
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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