2.5+Segment+Proofs

Chapter 2 Section 5: Segment Proofs (pgs. 102-107) This section of Chapter 2 will help teach how to prove statements about congruent segments. We will learn more about this by writing proofs. There is a new theorem that we will be learning, Theorem 2.1. This theorem is called "Properties of Segment Congruence". 2.1 Concludes that segment congruence is reflexive, symmetric, and transitive. For example: Vocabulary: Paragraph proof- Proof written in paragraph form Theorem 2.1- segment congruence is reflexive, symmetric, and transitive

Sample Problems =Example 1=
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/given_arrow.gif align="absmiddle"]] || [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_pq.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/congruent.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_xy.gif align="absmiddle"]] ||


 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/prove_arrow.gif align="absmiddle"]] || [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_xy.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/congruent.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_pq.gif align="absmiddle"]] ||



**(McDougal Littell, page 102)** Use the diagram and the given information to complete the missing steps and reasons in the proof.
 * =**Example 2**= || [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="10" height="20"]] || Using Congruence ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/given_arrow.gif align="absmiddle"]] || //LK// = 5, //JK// = 5, [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_jk.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/congruent.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_jl.gif align="absmiddle"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/prove_arrow.gif align="absmiddle"]] || [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_lk.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/congruent.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_jl.gif align="absmiddle"]] ||

(**McDougal Littell, page 103**)

In the diagram, //Q// is the midpoint of.
 * ||  ||   || =**Example 3**= || [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="10" height="20"]] || Using Segment Relationships ||



Show that //PQ// and //QR// are each equal to //PR//.

|| || //PQ// = //PR// and //QR// = //PR//. || (**McDougal Littell, page 103**)
 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] Decide what you know and what you need to prove. Then write the proof.[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]]|| [[image:http://images.classwell.com/ebooks/images/mcd_geo/given_arrow.gif align="absmiddle"]] || //Q// is the midpoint of [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_pr.gif align="absmiddle"]]. ||

=Additional Practice:= http://regentsprep.org/Regents/math/geometry/GP3/preproof.htm || =Extra help links:= http://library.thinkquest.org/2609/l2s3.htm http://www.themathlab.com/geometry/mathcourt/writeproofs.htm **Information used from McDougal Littell eEdition Plus**