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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! 2-Column Proof 2-Column • 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 2-column 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=6x-15 PR=46 Prove: x=7 1. 2. 3. 4. 5. 6. Statements PQ=2x+5, QR=6x-15, PR=46. PQ+QR=PR 2x+5+6x-15=46 8x-10=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 ...
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