4.2+Congruence+and+Triangles

Michael and Colin's Wiki (4.2) This Wiki will focus on the lesson 4.2 (Congruence and Triangles) Here are some main points
 * Brief summary of the topic Congruence and Triangles
 * 2 website that teach you the lesson and give you advice
 * 3 sample problems and solutions (Math-Type)
 * Vocabulary Terms and Theorems (including Diagrams)


 * In this wiki, we will be going over how some ways of how and when to know triangles are Congruent. This lesson will include rules, theorems and examples of the types of problems dealing with these rules and theorems.**

__//**Vocab**//__ Congruent- Two geometric figures are congruent if they have the exact same size and shape Corresponding angles- When 2 figures are congruent, the corresponding angles that are in corresponding positions are equal Corresponding sides-When 2 figures are congruent, the corresponding sides that are in corresponding positions are equal. __//**Theorems**// Theorem 4.3__: Third Angles Theorem This theorem states that if two angles in a triangle are congruent to two angles of another triangle, then the third angles are also congruent. __Theorem 4.4:__ Properties of Congruent Triangles Reflexive- Every trianle is congruent to itself Symmetric- If triangle ABC is congruent to triangle DEF, then triangle DEF is congruent to triangle ABC Transitive- If triangle ABC is congruent to triangle DEF, and triangle DEF is congruent to triangle XYZ, then triangle ABC is congruent to triangle XYZ __//**Sample Problems**//__ ΔABC≅ΔDEF** Congruent Sides: AB ≅ DE, BC ≅ EF, and CA ≅ FD**
 * __SECTION 1__**
 * 1)Write a congruence Statement for the following:[[image:congruent-2.gif width="244" height="136" align="right"]]
 * Congruent Angles: ∠A≅∠D, ∠B≅∠E, and ∠C≅∠F

In ΔABC and ΔDEF,** **∠A****≅****∠D, and** **∠B****≅****∠E. If ∠C is equal to 59 and ∠F is equal to 4x-5, what is the value of x? Solution: Step 1) Identify that the third angle in the triangles are congruent by the third angles theorem. Step 2) Form equation 4x-5=59 Step 3) Add 5 to each side 4x-5+5=59+5, you come to 4x=64 Step 4) Divide both sides by 4 4x/4=64/4 Step 5) Your answer is x=16
 * 2)Find the value of x

3)Find the value of x** Solution: Step 1) Recognize that ∠C****≅∠K by the Third angles theorem** 5x-2=48 Step 3) Add 2 to each side 5x-2+2=48+2, you come to 5x=50 Step 4) Divide each side by 5 5x/5=50/5 Step 5) Your answer is x=10
 * ∠A****≅****∠L, and ∠B****≅∠M. ∠C=48 and ∠K=5x-2.
 * Step 2) Form equation

__SECTION 2: Name the property that goes with each statement__**
 * ΔABC****≅****ΔABC- Reflexive Property**
 * ΔABC≅ΔDEF, then** **ΔDEF****≅****ΔABC**-**Symmetric Property**
 * ΔABC≅ΔDEF,** **ΔDEF****≅****ΔXYZ, then** **ΔABC≅ΔXYZ- Transitive Property**

__//**Websites and books that will teach you about the things in this wiki**//__ http://mrpilarski.wordpress.com/2009/11/01/proving-triangles-congruent-using-definition-of-congruent-triangles/ Online textbook, section 4.2, pg 202

__//**Websites with extra practice problems**//__ http://www.classzone.com/books/geometry/page_build.cfm?content=lesson2_ee_ch4&ch=4 -Then click on the link that says **click __here__ for extra practice** http://quizlet.com/414892/chapter-4-congruent-triangles-flash-cards/ -will quiz you on your knowledge of triangles, click on any of the options