Chapter 2, Section 1 Conditional Statements

Conditional Statement Also know as an “If-then” statement. If it’s Monday, then I will go to school. Hypothesis: it’s Monday Conclusion: I will go to school

Converse When you switch the hypothesis & conclusion in a conditional statement. If it’s Monday, then I will go to school. If I go to school, then it’s Monday.

Negation Make the statement negative. Statement m<A is acute. Negation m<A is not acute

Inverse When the hypothesis & conclusion is negated. If it’s Monday, then I will go to school. If it’s not Monday, then I will not go to school.

Contrapositive When you negate the hypothesis & conclusion of the converse. If it’s Monday, then I will go to school. If I do not go to school, then it is not Monday.

Equivalent Statements When two statements are both true or both false, then they are equivalent statements

Chapter 2, Section 2 Definitions & Biconditional Statements

Perpendicular Lines Two lines are perpendicular if they intersect and form a right angle.

Biconditional Statement

Chapter 2, Section 3 Deductive Reasoning

Uses facts, definitions and accepted properties in a logic order to write a logical argument. Did you discover it for yourself? Or did you take someone’s word for it?

Law of Detachment If there is a TRUE conditional statement, and the hypothesis is true, then the conclusion is true.

Law of Syllogism Just like the transitive property. If hypothesis, then conclusion is true If conclusion, then new conclusion is true. Then If hypothesis, then new conclusion must also be true. Example: If it’s a polygon w/ 3 sides, then it’s a triangle. If it’s a triangle, then the sum of the interior angles is 180⁰. If it’s a polygon w/ 3 sides, then the sum of the interior angles is 180⁰.

Chapter 2, Section 4 Reasoning with Properties from Algebra

Properties Addition: If a=b, then a+c=b+c Subtraction: If a=b, then a-c=b-c Multiplication: If a=b, then ac = bc Division: If a=b and c≠0, then a÷c=b÷c

Additional Properties Reflexive: For any real number a = a. Symmetric: If a = b, then b = a. Transitive: If a = b, and b = c, then a = c. Substitution: If a = b, the a can be substituted for b in any equation or expression.

Example 1

Example 2

Try on your own:

Properties of Equality Reflexive Property: For any segment AB, AB = AB. Symmetric Property: If AB = CD, then CD = AB. Transitive Property: If AB = CD, and CD = EF, then AB = EF.

Chapter 2, Section 5 Proving Statements about Segments

Create a 2 column proof Statements on the left side Reasons on the right side Always start w/ the Given Use the figure to help guide you & label it

Reasons 1. Given 2. Definition of congruent segments 3. Symmetric Property of Equality 4. Definition of congruent segments

Chapter 2, Section 6 Proving Statements about Angles

Property of Angle Congruence

Congruent Supplements Theorem

Congruent ComplementsTheorem

Linear Pair Postulate If two angles form a line, then they are supplementary.

Vertical Angle Theorem Two lines intersect. The opposite angles are called vertical angles & they are congruent to each other.