# 2 5 Reasoning in Algebra and Geometry 2

2 -5 Reasoning in Algebra and Geometry 2. 5 Reasoning in Alg and Geo

2. 5 Reasoning in Alg and Geo

Vocabulary • • • Property Reflexive Symmetric Transitive Distributive Congruence 2. 5 Reasoning in Alg and Geo

Properties of Equality. 2. 5 Reasoning in Alg and Geo

Remember that the distributive property is simply a fancy word for multiplying (just have to do it two times or more). Distribute means to give something away to multiple items. You can distribute just signs as well, so keep that in mind. 2. 5 Reasoning in Alg and Geo

Problem 1: What is the value of x? Justify each step. 2. 5 Reasoning in Alg and Geo

Problem 1 Solution: Statement Reason 2. 5 Reasoning in Alg and Geo

More Properties: * You must ALWAYS provide the reasons to your statements or no credit will be earned. 2. 5 Reasoning in Alg and Geo

PROOFS: A convincing argument that uses deductive reasoning. To make a strong argument you must not have gaps in your proof. A proof logically shows why a conjecture is true. Example: Statement D is true because statements A, B, and C followed a logical pattern allowing then for D to be true too. 2. 5 Reasoning in Alg and Geo

Steps for setting up a proof: 1. Write down the given as Statement and Reason 1. 2. If there is information regarding equal and congruency signs, fill that information into your picture 3. Look at your given, if there are vocabulary words in your given, those words should tell you something vital about your problem so write down what you learn from your vocabulary words in statements 2 -…. your reasons will usually be definition of ____. 4. From what you learned using your vocabulary indicate any equality or congruency statements within your picture. 2. 5 Reasoning in Alg and Geo

Steps for setting up a proof: 5. Look at your picture now, does it deal with angles or segments? If angles you will probably use angle addition postulate. If segments you will probably use segment addition postulate. (eventually this will not always be the case, but we want to write down what we are able to verify by the pictures arrangement) 6. Now you want to look at the several statements that you have made from the above steps and see if you can combine them to make a new statement. 7. That new statement may lead to what you want to prove or it may lead to an additional statement that may be needed for you to prove what you need to prove. 2. 5 Reasoning in Alg and Geo

This is the idea: 2. 5 Reasoning in Alg and Geo

Use a Two-Column Proof: 2. 5 Reasoning in Alg and Geo

Given Reflexive Property of Equality Addition Property of Equality Angle Addition Postulate Substitution Property 2. 5 Reasoning in Alg and Geo

Problem 2: 2. 5 Reasoning in Alg and Geo

Problem 2 Solution: Statement Reason 1. Given 2. Reflexive Property of Equality 3. Segment Additions Property 4. Segment Additions Property 5. Substitution Property 6. Equality Property 2. 5 Reasoning in Alg and Geo

Problem 3: 2. 5 Reasoning in Alg and Geo

Problem 3 Solutioin: Given Definition of Midpoint Substitution 2 x = 12 Division Property of Equality 2. 5 Reasoning in Alg and Geo

Lesson Check 2. 5 Reasoning in Alg and Geo

Lesson Check 2. 5 Reasoning in Alg and Geo

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