Deductive ReasoningGeometry Chapter 2
Vocabulary Converse-formed by interchanging the
hypothesis and the conclusion
Statement: If p, then q
Converse: If q, then p
VocabularyCounterexample-an example that can be found
for which the hypothesis is true and the conclusion is false.
Conditional If-then Statements/Conditional Statements
“If B is between A and C, then AB+BC=AC If Katie eats a lot, then Katie is fat.
Hypothesis is in RedConclusion is in Blue
Biconditional A statement that contains the words “if and only
if”.
3x=12 if and only if, x=4
Katie gets hyper in the morning if and only if she drinks coffee
Properties from Algebra
Geometry Ch.2 Section 2
Properties of EqualityAddition Property
If a=b and c=d, then a+c=b+d
Subtraction Property
If a=b and c=d then a-c=b-d
Multiplication Property
If a=b, then ca=cb
Division Property
If a=b and c≠0, then a/c=b/c
Properties from AlgebraSubstitution Property
If a=b, then either a or b may be substitute for the other in any equation (or inequality).
Reflexive Property
a=a
Symmetric Property
If a=b, then b=a
Transitive Property
If a=b, b=c, a=c
Distributive Property
a(b+c)=ab+ac
Properties of CongruenceReflexive Property –
Symmetric Property-
Transitive Property-
Proving TheoremsGeometry Ch.2 Lesson 3
VocabularyTheorem-statements that are proved
Postulates-statements that are accepted without proof
Midpoint Theorem If M is the midpoint of
line AB, then AM=1/2AB and MB=1/2AB
Proofs/Deductive Reasoning
Angle Bisector Theorem
If ray AD is the bisector of <CAB,
then m<CAD=1/2m<CABand m<DAB=1/2m<CAB
Theorems about Angles and
Perpendicular LinesGeometry Ch. 2 Lesson 4
VocabularyComplementary Angles-two angles whose
measures have the sum of 90 degrees.
Supplementary Angles-two angles whose measures have the sum of 180 degrees
Vertical Angles-two angles such that the sides of one angle are opposite rays to the sides of the other angle.
TheoremVertical Angles are congruent
Perpendicular LinesGeometry Chapter 2 Lesson 5
VocabularyPerpendicular Lines-two lines that intersect to
form right angles (90 degree angles).
Theorem If two lines are perpendicular, then they form
congruent adjacent angles
TheoremIf two lines form congruent adjacent angles,
then the lines are perpendicular.
Theorem If the exterior sides of two adjacent acute angles
are perpendicular, then the angles are complementary.
Planning A ProofChapter 2 Lesson 6
TheoremIf two angles are supplements of congruent
angles (or of the same angle), then the two angles are congruent.
TheoremIf two angles are complements of congruent
angles (or of the same angle), then the two angles are congruent.