Chapter 2 (2.1-2.6)

Conditionals/properties/Intro to proofs

Converse conditional

Switches the hypothesis and conclusion

Inverse conditional

Negates hypothesis and conclusion

Contrapositive

Switches and negates hypothesis and conclusion

Original statement is always the same T/F as:

Contrapositive

Converse conditional is always the same T/F as:

Inverse

Addition POE

if a=b then a+c=b+c (adding the same quantity to both sides of equation is allowed)

Subtraction POE

If a=b, then a-c=b-c (subtracting the same quantity to both sides of equation is allowed)

Multiplication POE

If a=b, then ac=bc (Multiplying the same quantity to both sides of equation is allowed)

Division POE

If a=b and c is not 0, then a/c=b/c (dividing the same quantity to both sides of equation is allowed)

Substitution POE

If a=b it can be replaced by b in any equation/expression

Simplifying or combinging like terms is substitution

Distributive property

a(b+c) = ab+ac

Reflexive property of equality or congruence

a=a

Symmetric property of equality or congruence

if a=b, then b=a (often used as last step in proofs)

Transitive property of equality or congruence

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

Definition of a midpoint

If M is the midpoint of line AB, then AM is congruent to MB

Midpoint Theorem

If M is the midpoint of line AB, then AM = 1/2AB and MB = 1/2AB

Definition of Angle Bisector

If ray BX is the bisector of angle ABC, then angle ABC is congruent to angle CBX

Angle Bisector Theorem

If ray BX is the bisector of angle ABC, then m angle ABX = ½ m andle ABC and m angle CBX = ½ m angle ABC

Definition of Complementary angles

The sum of 2 angles is 90 degrees

Definition of Supplementary Angles

The sum of 2 angles is 180 degrees

Vertical angle theorem

Formed by intersecting lines, across from one another

Definition of perpendicular lines

2 lines that intersect to form right angles

Theorem: what angles do 2 lines that are perpendicular form?

Congruent, adjacent angles

Theorem: Relationship of 2 acute adjacent, angles where the exterior sides are perpendicular

Complementary

Theorem: If 2 angles are supplements of congruent angles/or same angles, then…

They are congruent

Theorem: If 2 angles are complements of congruent/same angles, then…

They are congruent