This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 2.5 Proving Statements About Segments About
p. 102 Theorem Theorem
• A true statement that follows as a result of true other true statements. • All theorems MUST be proved! 2Column Proof 2Column
• Numbered statements and corresponding Numbered reasons in a logical order organized into 2 columns. columns. statements reasons statements 1. 1. 1. 2. 2. 2. 3. 3. 3. etc. etc. Theorem 2.1 Properties of Segment Congruence
• Segment congruence is reflexive, symmetric, & transitive. For any AB, AB ≅ AB. If AB ≅ BC and BC ≅ CD, then AB ≅ CD. If AB ≅ BC, then BC ≅ AB. Proof of symmetric part of thm. 2.1 (reflexive & transitive parts 2.1 are in HW) are
Statements 1. 1. 2. 3. Reasons 1. 2. 3. 4. Given Defn. of congruent segs. Symmetric prop of = Defn. of congruent segs. AB ≅ BC
AB = BC BC = AB BC ≅ AB Paragraph Proof Paragraph
• Same argument as a 2column proof, but each step is written as a sentence; therefore forming a paragraph. • See bottom of page 102 for an example. Ex: Given: PQ=2x+5 QR=6x15 PR=46 Prove: x=7
1. 2. 3. 4. 5. 6. Statements PQ=2x+5, QR=6x15, PR=46. PQ+QR=PR 2x+5+6x15=46 8x10=46 8x=56 x=7 R Q P Reasons 1. Given 1. 2. 3. 4. Seg + Post. Subst. prop of = Simplify + prop of = Ex: Given: Q is the midpoint of PR. PR Prove: PQ and QR =
2
1. 2. 3. 4. 5. 6. Statements Q is midpt of PR PQ=QR PQ+QR=PR QR+QR=PR 2QR=PR QR= PR 1. 2. 3. 4. 5. 6. Reasons Given Defn. of midpt Seg + post Subst. prop of = Simplify Division prop of = 2 PR 1. PQ= 2 1. Subst. prop Assignment Assignment ...
View
Full
Document
This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.
 Spring '11
 Jackson

Click to edit the document details