2.1 Patterns and Inductive Reasoning -Inductive Reasoning: is based off observable patterns -Conjecture: a conclusion based off inductive reasoning -Counterexample: an example that proves a conjecture incorrect

2.2 Conditional Statements -Conditional: if/then statements made up of a hypothesis and a conclusion -Hypothesis: the part following the if -Conclusion: the part following the then -Converse: switching the hypothesis and the conclusion

2.2 Conditional Statements -Inverse Statement: Negates both the hypothesis and conclusion of a conditional statement -Contrapostive: Switches the hypothesis and conclusion of a conditional statement and negates them

2.3-2.4 Biconditionals and Deductive Reasoning -Biconditional: when a conditional statement and its converse are both true, you can combine them as a true biconditional using if and only if (iff) -Deductive Reasoning: reasoning logically from given statements to a conclusion. -Law of Detachment: if a conditional is true and its hypothesis is true, then its conclusion is true -Law of Syllogism: if p  q is true, and q  r is true, then p  r is true

2.5 Reasoning in Algebra and geometry -Addition Property of Equality: If a = b, then a + c = b + c -Subtraction Property of Equality: If a = b, then a – c = b – c -Multiplication Property of Equality: If a = b, then a x c = b x c -Division Property of Equality: If a = b and c ≠ 0, then a/c = b/c

2.5 Reasoning in Algebra and geometry -Reflexive Property of Equality: a = a -Symmetric Property of Equality: If a = b, then b = a -Transitive Property of Equality: If a = b and b = c, then a = c -Substitution Property of Equality: If a = b, then b can replace a in any expression -Distributive Property of Equality: a(b + c) = ab + ac

2.5 Reasoning in Algebra and geometry -Reflexive Property of Congruence: segment AB is congruent to segment AB angle A is congruent to angle A Symmetric Property of Congruence: If segment AB is congruent to segment CD, then segment CD is congruent to segment AB If angle A is congruent to angle B, then angle B is congruent to angle A -Transitive Property of Congruence: If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C

2.6 Proving angles congruent -Theorem 2.1: The vertical angle theorem

2.6 Proving angles congruent -Paragraph Proof: a proof written as sentences in a paragraph. Ex. Given angles 1 and 2 are vertical angles, we will prove that angle 1 and angle 2 are congruent. By the angle addition postulate, angle 1 plus angle 3 equals 180* and angle 2 plus angle 3 equals 180*. By substitution, angle 1 plus angle 3 equals angle 2 plus angle 3. Subtracting angle 3 from each side, you get angle 1 equals angle 2. We have proved the vertical angle theorem.

2.6 Proving angles congruent -Theorem 2.2: congruent supplement theorem says if 2 angles are supplements of the same angle (or of congruent angles), then the 2 angles are congruent (proof similar to VAT) -Theorem 2.3: congruent complement theorem says if 2 angles are complements of the same angle (or of congruent angles), then the 2 angles are congruent -Theorem 2.4: all right angles are congruent -Theorem 2.5: if 2 angles are congruent and supplementary, then each is a right angle

3.1 Lines and angles -Parallel Lines: coplanar lines that do not intersect -Parallel Planes: planes that do not intersect -Skew Lines: noncoplanar lines that do not intersect

3.1 Lines and angles -Transversal: a line that intersects two coplanar lines at 2 distinct points -Alternate Interior: angles 4 and 6 -Same Side Interior: angles 4 and 5 -Corresponding: angles 4 and 8

3.2 Properties of Parallel Lines If a transversal intersects two parallel lines, then… -Postulate 3.1: Corresponding angles Postulate says corresponding angles are congruent -Theorem 3.1: Alternate Interior angles Theorem says Alt Int angles are congruent -Theroem 3.2: Same Side Interior angles Theorem says same side Int angles are supplementary -Theorem 3.3: Alternate Exterior angles Theorem says alt ext angles are congruent (angles 1 and 8) -Theorem 3.4: Same Side Exterior angles Theorem says same side ext angles are supplemntary (angles 1 and 7)

3.3 Proving Lines Parallel -Postulate 3.2: Converse of the Corresponding Angles Postulate says if 2 lines and a transversal form corresponding angles that are congruent, then the 2 lines are Parallel -Theorem 3.5: Converse of the Alternate Interior angles Theorem says if 2 lines and a transversal form Alt Int angles that are Congruent, then the 2 lines are parallel -Theroem 3.2: Converse of the Same Side Interior angles Theorem says if 2 lines and a transversal form Same Side Int angles that are Supplementary, then the 2 lines are

3.3 Proving Lines Parallel -Theorem 3.7: Converse of the Alternate Exterior angles Theorem says if 2 lines and a transversal form Alt Ext angles that are Congruent, then the 2 lines are parallel -Theroem 3.8: Converse of the Same Side Exterior angles Theorem says if 2 lines and a transversal form Same Side Ext angles that are Supplementary, then the 2 lines are parallel

3.4 Parallel and Perpendicular Lines -Theorem 3.9: If 2 lines are parallel to the same line, then they’re parallel to each other -Theorem 3.10: In a plane, if 2 lines are perpendicular to the same line, then they’re parallel to each other -Theorem 3.11: In a plane, if a line is perpendicular to 1 of 2 parallel lines, then it is also perpendicular to the other

3.5 Parallel lines and triangles -Theorem 3.12: The angles of a triangle sum to 180 degrees -Exterior Angle of a Polygon: An angle formed by a side and an extension of an adjacent side -Remote Interior Angles: the two Non-adjacent interior angles -Theorem 3.13: The Triangle Exterior Angle theorem says the measure of Each exterior angle equals the sum of the measures of the two remote interior angles

3.8 Slopes of Parallel and Perpendicular Lines -Slopes of Parallel Lines: If 2 nonvertical lines are parallel, then their slopes are equal If the slopes of 2 distinct nonvertical lines are equal, the lines are parallel Any 2 vertical lines are parallel -Slopes of Perpendicular Lines: If 2 nonvertical lines are perpendicular, the product of their slopes is -1 If the slopes of 2 lines have a product of -1, the lines are perpendicular Any horizontal line and vertical line are perpendicular