2-5 Reasoning in Algebra and Geometry “why do we know what we know about something”

Properties of Equality.

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.

In your homework if a problem looks like they are combining like variable terms you will use the distributive property as your reason. Example. Step 1. (2x + 30) + x = 180 Step 2. 3x+30 = 180 Distributive Property The math that is happening is the use of the associative and commutative properties to rewrite the problem as (2x+x)+30 =180. And then factoring out an x from (2x+x)+30=180 to get x(2+1)+30=180 which then simplifies to x(3)+30=180 then using the distributive property you get 3x+30=180.

Some things that we already know about CONGRUENCY

Transitive property The transitive property is a linking concept that links multiple parts to one another and if they are all congruent then the first item stated in the linkage would be congruent to the last item stated in the linkage.

Lets identify some properties of equality and congruency.

Whenever we try to make an argument you must have a valid reason for your argument what statements allow you to go from statement A to statement B.

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. Statement D is true because statements A, B, and C followed a logical pattern allowing then for D to be true too.

This is what we call a 2 column proof.

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. 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.

This is the idea behind step 5 on the previous slide.

MATHXL HWK 2.5