Ex 1). Look for a Pattern. What Are the Next Two Terms in Each Sequence?

2.1: ______Date: ______Geometry

______is reasoning based on patterns you observe. Ex 1). Look for a pattern. What are the next two terms in each sequence? a) 4, 8, 16, 32, … b)

A ______is used to find the tenth or one-hundredth term in a sequence, it’s a conclusion you reach using inductive reasoning. Ex 2). a) What conjecture can you make about the 25th term in 1, 2, 3, 1, 2, 3, … ?

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

*It is important to gather enough information before making a conjecture. Ex 3). a) What conjecture can you make about the sum of the first 40 even numbers?

b) What conjecture can you make about the sum of the first 30 even numbers?

Ex 4). Sales of lift tickets at a ski resort increased over a period of four consecutive months. What conjecture can you make about the number of lift tickets the resort will sell in February? Not all conjectures are true, you should check it multiple times to be sure. You can prove that a conjecture is ______by finding ______. A counterexample is an example that shows that a conjecture is ______. Ex 5). What is a counterexample for each conjecture? a) If an animal is green, it is a frog.

b) Any three segments form a triangle.

c) When you multiply a number by 2, the product is divisible by 4.

d) If a flower is red, it is rose.

e) One and only one plane exists through any three points.

f) When you multiply a number by 3, the product is divisible by 6.

Homework: pg. 93 #1 – 3, 6 – 14(e), 18 – 27, 29, 30, 32, 33 – 40 2.2 Day 1: ______Date: ______Geometry

A Conditional Statement is an ______statement.

The ______is the part _____ following if.

The ______is the part _____ following then.

Ex 1). What are the hypothesis and the conclusion of the conditional statement? a) If a number is even, then it is divisible by 2. Hypothesis: ______Conclusion: ______

b) If an angle measures 130, then the angle is obtuse. Hypothesis: ______Conclusion: ______

Ex 2). How can you write the following statement as a conditional? a) Adjacent angles share a side.

b) Dolphins are mammals.

The ______of a conditional statement is either true or false. * To show the statement is true: show that every time the hypothesis is true, the conclusion is true. * To show that a statement is false: find ______counterexample for which the hypothesis is true, but the conclusion is false. Ex 3). Is the conditional true or false? If it is false, find a counterexample. a) If you live in Copley, then you live in Ohio.

b) If a number is divisible by 5, then it is odd.

c) If a month 28 days, then it is February.

d) If two angles form a linear pair, then they are supplementary.

Homework: pg. 99 #1, 3 – 13, 14 – 28(e) 2.2 Day 2: ______Date: ______Geometry

The ______of a statement p is the ______of the statement. The symbol ______is read “not p.”

Statement How to Write It Example Symbols How to Read It

Conditional

Converse

Inverse

Contrapositive

Truth Values: Statement Example Truth Value Conditional Converse Inverse Contrapositive

Ex 1). What are the converse, inverse, and contrapositive of each of the conditional statements below? What are the truth values of each?

a) If a figure is a rectangle, then it is a parallelogram.

b) If a vegetable is a carrot, then it contains beta carotene.

Homework: pg. 103 #1, 3 – 7, 11 – 14, 18 – 25 2.3: ______Date: ______Geometry

A ______is a single true statement that combines a true conditional and its true converse. You can write a biconditional by joining the two parts of each conditional with the phrase ______.

Ex 1). What is the converse of the following true conditional? If the converse is also true, combine the statements as a biconditional.

Conditional: If the sum of the measures of two angles is 90, then the angles are complementary. A biconditional combines and as ______. ex: A point is a midpoint if and only if it divides a segment into two congruent segments.

Ex 2). What are the two conditional statements that form this biconditional?

Two numbers are additive inverses if and only if their sum is 0.

What makes a good definition?

1. A good definition uses ______terms.

2. A good definition is ______.

3. A good definition is ______. It can be written as a true ______.

Ex 3). Is this definition of an equilateral triangle reversible? If yes, write it as a true biconditional.

An equilateral triangle is a triangle with 3 congruent sides. Ex 4). Which of the following is a good definition?

[A] Dogs are animals with 4 paws.

[B] Squares have 4 sides.

[C] Tuesday is the day before Wednesday.

[D] An acute angle has a small measure.

Homework: pg. 108 #1 – 3, 8 – 26(e), 45 – 50 2.4: ______Date: ______Geometry

______is the process of reasoning ______from given statements or facts to make a ______.

Law of ______: If the hypothesis of a ______conditional is ______, then the conclusion is ______.

Ex 1). What can you conclude from the given true statement? a) Given: If it is raining outside, then there are clouds in the sky. It is raining today.

b) Given: If Malcolm scores at least 85% on his final exam, then he will earn an A for the term. Malcolm scores a 90% on his final exam. c) Given: If two angles are vertical, then they are congruent. Angles 3 and 4 are vertical angles.

Law of ______: Symbols: Examples:

Ex 2). What can you conclude from the given information? a) Given: If a number is divisible by 12, then it is divisible by 6. If a number is divisible by 6, then it is divisible by 3.

b) Given: If a figure is a square, then the figure is a parallelogram. If a figure is a rectangle, then the figure is a parallelogram.

Ex 3). What can you conclude from the given information?

a) Given: If you live in Cincinnati, then you live in Ohio. If you live in Ohio, then you live in the United States. Ken lives in Cincinnati.

b) If a river is more than 4000 mi long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 mi long. Homework: pg. 117 #1 – 3, 6 – 16(e), 19 – 24, 26, 28 2.5: ______Date: ______Geometry

Ex 1). What is the value of x?

Ex 2). Use the distributive property to solve each of the following. Justify your steps. a) 3(2x – 8) = 6 b) 4(x – 7) – 2(3x + 4) = 2 Ex 3). What is the name of the property of equality or congruence that justifies going from the first statement to the second statement?

a) 7x + 3 = 24 b) RS = ST and ST = TU 7x = 21 RS = TU

c) 5x = 10 b) 3x – 4 = x and x = -2 10 = 5x 3(-2) – 4 = -2

A ______is a convincing argument that uses deductive reasoning. A proof ______shows why a conjecture is true. A ______lists each statement on the left and the reason (justification) on the right. Each statement must follow logically from the steps ______it. Ex 4). Write a two-column proof. Given: AC = BD Prove: AB = CD

Ex 5). Write a two-column proof. Given: Prove: Homework: pg. 124 #1 – 17 2.6: ______Date: ______Geometry

A ______is a conjecture or statement that you prove ______

Ex 1). What is the value of x? a) b)

Ex 2). Write a two column proof: Given: Prove:

Ex 3). Write a two-column proof: Given:

Prove: Ex 4). Write a two-column proof: Given: Prove: Homework: pg. 132 #1 – 3, 6 – 13, 16 – 17, 19