2-5+Segment+Proofs


 * Found in textbook pages: p.102-107**

In this section we first learned about the basic theorems, a true statement that follows as a result of other true statements.(p.102) These theorems must be proved by using a paragraph proof, paragraph proof and two-column proof which has numbered statements and reasons that show the logical order of an argument.(p.102) You will be given information that will lead you to a conclusion you are asked to come to.The three properties of segment congruence are reflexive, symmetric and transitive.(p. 102) This will help you prove segment concurrency while putting it into an organized proof.

for help with different types of proofs: http://regentsprep.org/Regents/math/geometry/GP3/styleofproof.htm

for help with properties: http://hotmath.com/hotmath_help/topics/reflexive-symmetric-transitive-properties.html

**Reflexive Property: for any segment AB, AB≅AB. Every segment measurement is equal to itself**

**Symmetric Property: If AB≅CD, then CD≅AB. That is if one measurement is equal to another, then you can flip them and still be equal**

**Transitive Property: if AB≅CD, and CD≅EF, then AB≅EF.**
 * if whenever an element //a// is related to an element //b//, and //b// is in turn related to an element //c//, then //a// is also related to //c//.**

1.) The symmetric property of equality given: PQ is congruent to XY prove: XY is congruent to PQ (From Note sheet)
 * Statements || Reasons ||
 * PQ is congruent to XY || Given ||
 * PQ = XY || definition of congruent statements ||
 * XY = PQ || symmetric property of equality ||
 * XY is congruent to PQ || Definition of congruency ||



2.) Given: AC = BD Prove: AB ≅ CD BD =BC +CD || Segment Addition Postulate || FROM NOTES
 * Statements || Reasons ||
 * AC= BD || GIVEN ||
 * AC = AB + BC
 * AB + BC = BC +CD || Substitution/transitive property of equality ||
 * AB =CD || Subtraction property ||
 * AB ≅ CD || Definition of Congruence ||

3.) given: B is between A and D C is between A and D Prove: AB+ BD = AC +CD

C is between A and D || Given ||
 * Statements || Reasons ||
 * B is between A and D
 * AB + BC = AD || segment addition postulate ||
 * AC +CD= AD || segment addition postulate ||
 * AD = AC +CD || symmetric property of equality ||
 * AB + BD = AC +CD || Transitive property of equality ||


 * More Vocab:**

__Theorem__: a true statement that needs to be proven.

__Two-Column proof:__ A way of organizing a proof that has numbered statments and reasons that show the logical order of an argument. ex.) It has it's statements and reasons. From http://www.utdanacenter.org/mathtoolkit/images/activities/geo_b3b_table.gif

__Paragraph Proof__: a way of organizing a proof that you put all your statements and reasons into a logical order in a paragraph.

Ex.) See how they put all their reasons and staments in a paragraph. from http://2.bp.blogspot.com/_k2L8s-MfQQQ/TOPrmPF7UGI/AAAAAAAAAA0/5Ac7jKiTAxk/s1600/dodo.PNG



1.) An example of the symmetric Property of segments congruence is "If AB≅ ?, then CD≅?" (from the textbook) 2.) In transitive property, If AB≅BC, BC≅GF, then ? ≅ ? 3.) In reflexsive property, If segments AB, the ?≅? 4.) Solve for the variable using the given information. explain your steps in a 2 column proof. (for more problems like this go to page 105 #s 8-11) (this is #8)
 * For more practice:**

If AB≅BC, CD≅BC

AB= 2x+1 CD=4x-11

For more Practice problems go to page 104-107. the odd answers are in the back of the book and look over your notes. Good Luck!