Welcome to class. Here’s your warm up: Write the conditional, converse, inverse and contrapositive of the following statement: If it’s raining, then the grass is wet. Write the converse of the following statement and if it’s true, please write the biconditional: If a polygon is a triangle, then it has three sides. Please give an example of inductive reasoning. Draw an Euler for the following situation: If he’s a singer, then he’s a musician. Nicole is a singer.

Daily Quiz #2 1. Which law is this and what conclusion can you draw? If you wear a headband then you have school spirit. Vanesa is wearing a headband. Which law is this and what conclusion can you draw? If you eat your boogers, then you will get fat. If you get fat, then you won’t get asked to homecoming. If you can, write the biconditional for the following sentence. If you can’t, tell why not. If it’s raining, then the grass is wet.

A closed three sided figure is a triangle. Welcome to class. Here’s your warm up: Write the conditional, converse, inverse and contrapositive of the following statement. If you can, write the biconditional; if you can’t tell why not. A closed three sided figure is a triangle. If possible, give the conclusion and tell which law describes the following: a. If she behaves then she will get candy. Saundra is eating candy. b. If Shananigans does her homework then she will pass the test. If she passes the test then she can get her driver’s license.

Daily Quiz #3 Taylor has blonde hair. 1. Write the conditional, converse, inverse and contrapositive of the following statement. If you can, write the biconditional; if you can’t tell why not. Taylor has blonde hair. 2. If possible, give the conclusion and tell which law describes the following: a. If it’s Monday, then it’s meatloaf. We are eating meatloaf. b. If Lindsay eats her peas, then she will get strong. If Lindsay is strong, then she will win at arm wrestling.

2.5 Reasoning in Algebra and Geometry We accept postulates as true. We also accept the properties of equality from algebra as true.

Other things we know are true We know the distributive property is true: And these properties of congruence:

Let’s learn to justify our steps using properties What gives us permission to go from step 1 to step 2? “Permission” means ‘what property justifies the step’. Distributive property 1. 3(x + 2) = 15 2. 3x + 6 = 15 Subtraction property of equality 3x + 6 = 15 3x = 9 Division property of equality 3x = 9 x = 3 Good job! Let’s keep going

Great! let’s try this with geometry What gives us permission to go from step to step? 1. 2x + 5(x + 1) = 6x - 4 2x + 5x + 5 = 6x – 4 7x + 5 = 6x – 4 7x = 6x – 9 x = -9 1. Given Distributive Property Addition Property Subtraction Property of Equality Great! let’s try this with geometry

FIRST THING IS TO MARK THE DRAWING We are given the information that KM = 35 and we want to show that KL = 15 35 FIRST THING IS TO MARK THE DRAWING ALWAYS!!! Then, begin formulating a plan…

35 1. KM = 35 KL + LM = KM (2x – 5) + 2x = 35 4x – 5 = 35 4x = 40 we want to show that KL = 15 35 1. KM = 35 KL + LM = KM (2x – 5) + 2x = 35 4x – 5 = 35 4x = 40 x = 10 KL = 2x – 5 KL = 2(10) – 5 KL = 15 1. Given Segment addition postulate Substitution property Addition property Addition property of equality Division property of equality Given Order of Operations

Justifying Steps When Solving an Equation (2x + 30)◦ x◦ A O C M What is the value of x? Justify each step. <AOM and <MOC are supplementary m<AOM + m<MOC = 180 (2x + 30) + x = 180 3x +30 = 180 3x = 150 X = 50 Angles that form a linear pair are supplementary Definition of supplementary <s Substitution Property Combine like terms Subtraction Property of Equality Division Property of Equality

PROOF This will be your new best friend. Spend a lot of time with it ♥ A proof is a convincing argument that uses deductive reasoning. A proof logically shows why a conjecture is true. A two-column proof lists each statement on the left and the justification, or reason, on the right. Each statement must follow logically from the steps before it.

Two-Column Proof

Practice 2.5 and 2.6 Cross off 11 on 2.5 2.6 should be one-sided Your assignment Practice 2.5 and 2.6 Cross off 11 on 2.5 2.6 should be one-sided