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.