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Deductive ReasoningGeometry Chapter 2
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Vocabulary Converse-formed by interchanging the
hypothesis and the conclusion
Statement: If p, then q
Converse: If q, then p
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VocabularyCounterexample-an example that can be found
for which the hypothesis is true and the conclusion is false.
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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
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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
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Properties from Algebra
Geometry Ch.2 Section 2
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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
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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
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Properties of CongruenceReflexive Property –
Symmetric Property-
Transitive Property-
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Proving TheoremsGeometry Ch.2 Lesson 3
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VocabularyTheorem-statements that are proved
Postulates-statements that are accepted without proof
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Midpoint Theorem If M is the midpoint of
line AB, then AM=1/2AB and MB=1/2AB
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Proofs/Deductive Reasoning
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Angle Bisector Theorem
If ray AD is the bisector of <CAB,
then m<CAD=1/2m<CABand m<DAB=1/2m<CAB
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Theorems about Angles and
Perpendicular LinesGeometry Ch. 2 Lesson 4
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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.
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TheoremVertical Angles are congruent
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Perpendicular LinesGeometry Chapter 2 Lesson 5
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VocabularyPerpendicular Lines-two lines that intersect to
form right angles (90 degree angles).
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Theorem If two lines are perpendicular, then they form
congruent adjacent angles
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TheoremIf two lines form congruent adjacent angles,
then the lines are perpendicular.
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Theorem If the exterior sides of two adjacent acute angles
are perpendicular, then the angles are complementary.
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Planning A ProofChapter 2 Lesson 6
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TheoremIf two angles are supplements of congruent
angles (or of the same angle), then the two angles are congruent.
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TheoremIf two angles are complements of congruent
angles (or of the same angle), then the two angles are congruent.