Deductive Reasoning Geometry Chapter 2

Vocabulary Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse: If q, then p

Vocabulary Counterexample-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 Red Conclusion 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 Equality Addition 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 Algebra Substitution 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 Congruence Reflexive Property – Symmetric Property- Transitive Property-

Proving Theorems Geometry Ch.2 Lesson 3

Vocabulary Theorem-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<CAB and m<DAB=1/2m<CAB

Theorems about Angles and Perpendicular Lines Geometry Ch. 2 Lesson 4

Vocabulary Complementary 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.

Theorem Vertical Angles are congruent

Perpendicular Lines Geometry Chapter 2 Lesson 5

Vocabulary Perpendicular Lines-two lines that intersect to form right angles (90 degree angles).

Theorem If two lines are perpendicular, then they form congruent adjacent angles

Theorem If 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 Proof Chapter 2 Lesson 6

Theorem If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.

Theorem If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.