2.1: Patterns and Inductive Reasoning

Look for a pattern. What are the next 2 terms in the sequence? 3, 9, 27, 81, …

Look at the circles. What conjecture can you make about the number of regions 20 diameters form?

What conjecture can you make about the 21st term in R, W, B, R, W, B, …

Sales of backpacks decreased over the past 6 months Sales of backpacks decreased over the past 6 months. What conjecture can you make about the number of backpacks the company will sell in May?

What is a counterexample for each conjecture? If the name of a month starts with the letter J, then it is a summer month. You can connect any 3 points to form a triangle. When you multiply a number by 2, the product is greater than the original number. If a flower is red, then it is a rose.

2.2: Conditional Statements

What are the hypothesis and conclusion of the conditional? If an animal is a robin, then the animal is a bird. If an angle measure 130°, then the angle is obtuse.

How can you write the following as a conditional statement. Vertical angles share a vertex. Dolphins are mammals.

Truth Values: Is the conditional true or false Truth Values: Is the conditional true or false? If it is false, find a counterexample. If a woman is French, then she is European. If a number is divisible by 3, then the number is odd. If a month has 28 days, then it is February.

What are the converse, inverse, and contrapositive of the conditional What are the converse, inverse, and contrapositive of the conditional? What are the truth values of each? If false, find a counterexample. If a figure is a square, then the figure is a quadrilateral.

2.3: Biconditionals and Definitions

What is the converse of the true conditional What is the converse of the true conditional? If the converse is also true, then write the statement as a biconditional. If the sum of the measures of two angles is 180, then the two angles are supplementary.

What are the 2 conditional statements that form this biconditional? A ray is an angle bisector if and only if it divides an angle into two congruent angles.

Is this definition of quadrilateral reversible Is this definition of quadrilateral reversible? If yes, write it as a true biconditional. Definition: A quadrilateral is a polygon with 4 sides.

Which of the following is a good definition?

2.4: Deductive Reasoning

What can you conclude from the given true statements? If a student gets an A on a final exam, then the students will pass the course. Felicia got an A on her History final. If a figure is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides.

2-5: Reasoning in Algebra and Geometry

What is the value of x? Justify each step.

What is the name of the property of equality or congruence that justifies going from the first step to the second?

Write a 2-Column Proof Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4.

2-6: Proving Angles Congruent

What is the value of x?

Write a 2-Column Proof Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4.

Writing a Paragraph Proof