geometric proofs

all proof definitions of are biconditionals -><-

congruent complements theorem

if two angles are complements of congruent angles (or of the same angle), then the two angles are congruent

perpendicular lines def

two lines that intersect to form right angles

perpendicular lines theorem

if two lines are perpendicular, then they from congruent adjacent angles

converse of perpendicular lines theorem

if two lines form congruent adjacent angles, the lines are perpendicular

perpendicular lines complementary theorem

if the exterior sides of two adjacent angles are perpendicular, then the angles are complementary

midpoint def

if m is the midpoint of line AB, then line AM is congruent to line MB

midpoint theorem

if m is the midpoint of line AB then AM = ½ of AB or MB = ½ of AB

angle bisector def

if ray BX is the angle bisector of angle ABC then angle ABX is congruent to angle XBC

angle bisector theorem

if ray BX is the angle bisector of angle ABC the measure of ABX = ½ measure ABC and the measure of XBC is ½ of the measure ABC

substitution POE

if a = b, then either a or b may be substituted for the other in any equation or inequality

reflexive POE

a = a

symmetric POE

if a = b, then b = a

transitive POE

if a = b and b = c, then a = c

reflexive POC

DE is congruent to DE and angle D is congruent to angle D

symmetric POC

if line DE is congruent to line FG, then line FG is congruent to line DE / if angle D is congruent to angle E, then angle E is congruent to angle D

transitive POC

if line DE is congruent to line FG and line FG is congruent to line JK, then line DE is congruent to line JK / if angle D is congruent to angle E and angle E is congruent to angle F, then angle D is congruent to angle F

addition POE

if a = b and c = d, then a + c = b + d

subtraction POE

if a = b and c = d, then a - c = b - d

multiplication POE

if a = b, then ca = cb

division POE

if a = b and c does not equal to 0, a/c = b/c

vertical angle theorem

vertical angles are congruent

segment addition postulate

if B is between A and C, then AB + BC = AC

angle addition postulate

the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together