Reasoning+with+Algebra,+4

Reasoning With Algebra Amanda K, Andie D & Caroline F       Postulate 1-ruler postulate Postulate 2- segment addition postulates Postulate 3- protractor postulates Postulate 4- angle addition postulates Postulate 5-through any two points exists exactly one line. Postulate 6- a line that contains at least 2 points. Postulate 7-if two lines intersect, then their intersection is exactly one point. Postulate 8- through any non-collinear points there exists exactly one plane. Postulate 9-a plane contains at least 3 non-collinear points. Postulate 10- if two points lie in a plane, the the line containing them lies in the plane. Postulate 11- if two planes intersect then the intersection is the line. Linear Pair Postulate- two adjacent angles whose non-common sides are opposite rays.
 * Postulates: **

Congruence of Segments- line segments that are the same length. <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Congruence of Angles- angles that have the same measure <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Right Angles Congruence Theorem-all right angles are congruent <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Congruent Supplements Theorem- if two angles are supplementary to the same angle, then they are congruent <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Congruent Complements Theorem- if two angles are complementary to the same angle, then they are congruent <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Vertical Angles Congruence Theorem- vertical angles are congruent
 * <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Theorems: **

<span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Addition Property: If 2=2, then 2 + 3=2 + 3 <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Subtraction Property: If 2=2, then 2 – 3=2 - 3 <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Multiplication Property: If 2=2, then 2(3)= 2(3) <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Division Property: If 2=2, then 2/1=2/1 <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> Substitution Property: If 2=2, then 2 can be substituted for 2 in any equation or expression. <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Distributive Property- a(b+c)= ab+ac, where a, b and c are real numbers <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Reflexive Property of Equality-for real numbers a, a=a <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Symmetric Property of Equality-if a = b, then b= a <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Transitive Property of Equality- if a = b then b= c, then a= c
 * <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Algebraic Properties: **

//<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 140%;">Steps for Writing Proofs: //

<span style="background-color: transparent; border: medium none; color: #000000; display: block; overflow: hidden; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; border-bottom: medium none; border-top: medium none; color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 120%; overflow: hidden;">**1. Get or create the statement of the theorem.** The statement is what needs to be proved in the proof itself. Sometimes this statement may not be on the page. That's normal, so don't fret if it's not included. If it's missing in action, you can create it by changing the geometric shorthand of the information provided into a statement that represents the situation. The given is the hypothesis and contains all the facts that are provided. The given is the what. What info have you been provided with to solve this proof? The given is generally written in geometric shorthand in an area above the proof. They say a picture is worth a thousand words. You don't exactly need a thousand words, but you do need a good picture. When you come across a geometric proof, if the artwork isn't provided, you're going to have to provide your own. Look at all the information that's provided and draw a figure. Make it large enough that it's easy on the eyes and that it allows you to put in all the detailed information. Be sure to label all the points with the appropriate letters. If lines are parallel, or if angles are congruent, include those markings, too. The last line in the statements column of each proof matches the prove statement. The prove is where you state what you're trying to demonstrate as being true. Like the given, the prove statement is also written in geometric shorthand in an area above the proof. It references parts in your figure, so be sure to include the info from the prove statement in your figure. The proof is a series of logically deduced statements — a step-by-step list that takes you from the given; through definitions, postulates, and previously proven theorems; to the prove statement. <span style="background-color: transparent; border: medium none; color: #000000; display: block; overflow: hidden; text-align: left; text-decoration: none;"> <span style="background-color: transparent; border: medium none; color: #000000; display: block; overflow: hidden; text-align: left; text-decoration: none;"> <span style="background-color: transparent; border: medium none; color: #000000; display: block; overflow: hidden; text-align: left; text-decoration: none;"> Example Problems:
 * 2. State the given.**
 * 3. Get or create a drawing that represents the given.**
 * 4. State what you're going to prove.**
 * 5. Provide the proof itself.**

1.







5. Ex: Solve the equation & write a reason for each step.

2(3x+1)=5x+14 Given 6x+2=5x+14 Distributive prop x+2=14 Subtraction prop of = x=12 Subtraction prop of

**Website for review :** **http://www.mathwarehouse.com/geometry/congruent_triangles/isosceles-triangle-theorems-proofs.php** **Powerpoint:** **http://www.mrperezonlinemathtutor.com/G/1_3_Proofs_Segments_Angle_Relationships.html**