Theorem Thursday 2 Flashcards
Addition property of equality
If a=b then a+c=b+c
Subtraction property of equality
If a=b then a-c=b-c
Multiplication property of equality
If a=b then a•c=b•c c cannot equal 0
Division property of equality
If a=b then a/c=b/c c cannot equal 0
Distributive property
a(b+c)=ab+ac
a(b-c)=ab-ac
Reflexive property of equality
a=a
Symmetric property of equality
If a=b then b=a
Transitive property of equality
If a=b and b=c them a=c
Substitution property of equality
If a=b then a can be substituted for b or b for a in any equation or expression
Properties of segment congruence
REFLEXIVE: for any segment AB, segment AB is congruent to segment AB
SYMMETRIC: if segment AB is congruent to segment CD then segment CD is congruent to segment AB
TRANSITIVE: if segment AB is congruent to segment CD and segment CD is congruent to segment EF then segment AB is congruent to segment EF
Properties of angle congruence
REFLEXIVE: for any angle A, angle A is congruent to angle A
SYMMETRIC: if angle A is congruent to angle B then angle B is congruent to angle A
TRANSITIVE: if angle A is congruent to angle B and angle B is congruent to angle C then angle A is congruent to angle C
Right angles congruence theorem
All right angles are congruent
Congruent supplements theorem
If two angles are supplementary to the same angle or two congruent angles then they are congruent
Congruent complements theorem
If two angles are complementary to the same angle or two congruent angles then they are congruent
Vertical angles congruence theorem
Vertical angles are congruent
Parallel postulate
If there is a line and a point not on the line then there is exactly one line through the point parallel to the given line
Perpendicular postulate
If there is a line and a point not on the line then there is exactly one line through the point perpendicular to the given line
Corresponding angles theorem
If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent
Alternate interior angles theorem
If two parallel lines are cut by a transversal then the pair is alternate interior angles are congruent
Alternate exterior angle theorem
If two parallel lines are cut by a transversal then the pairs of alternate exterior angles are congruent
Consecutive interior angles theorem
If two parallel lines are cut by a transversal then the pairs of consecutive interior angles are supplementary
