equal quantities plus equal quantities are equal
any given quantity equals itself
equal quantities minus equal quantities are equal
if one quantity equals a second and the second equals a third, then the first equals the third
construct line segement
if a line segment is given, then another line segment can be constructed equal to it
if a line segment is given, then its midpoint can be determined
if an angle is given, the an angle can be constructed equal to it
if an angle is given, then its bisector can be constructed
if a triangle has two sides equal, then the angles opposite these sides are equal
if a point is not on a line segment, then a perpendicular from the point to the line segment can be constructed
equal quantities multiplied or divided by equal quantities are equal
with a straightedge, any given line segment can be extended
if perpendicular then ninety degrees
if ninety degrees then perpendicular
if a transversal forms equal alt. interior angles with two line segments, then the line segments form parallels
vertical angles are equal
any whole quantity equals the sum of its parts
there is exactly one parallel to a given line through a point that is not on the line
if two lines are parallel then the alt. interior angles are equal
if a transversal form equal corresponding angles with two line segments, then the line segments are parallel
if two lines are parallel then he corresponding angles are equal
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