Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Analytic geometry wikipedia , lookup
Shape of the universe wikipedia , lookup
Cartan connection wikipedia , lookup
Algebraic geometry wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Line (geometry) wikipedia , lookup
Geometrization conjecture wikipedia , lookup
2-7 2-7 Flowchart Flowchartand andParagraph ParagraphProofs Proofs Warm Up Lesson Presentation Lesson Quiz Holt Geometry Holt Geometry 2-7 Flowchart and Paragraph Proofs Warm Up Complete each sentence. 1. If the measures of two angles are ? , then the angles are congruent. equal 2. If two angles form a ? , then they are supplementary. linear pair 3. If two angles are complementary to the same angle, then the two angles are Holt Geometry ? . congruent 2-7 Flowchart and Paragraph Proofs Objectives Write flowchart and paragraph proofs. Converse Postulates Holt Geometry 2-7 Flowchart and Paragraph Proofs Vocabulary flowchart proof paragraph proof Holt Geometry 2-7 Flowchart and Paragraph Proofs Note 37 A second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof. The justification for each step is written below the box. Holt Geometry 2-7 Flowchart and Paragraph Proofs Example 1: Reading a Flowchart Proof Given: 2 and 3 are comp. 1 3 Prove: 2 and 1 are comp. Flowchart proof: Holt Geometry 2-7 Flowchart and Paragraph Proofs Note 37 (cont.) A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step. Holt Geometry 2-7 Flowchart and Paragraph Proofs Example 3: Reading a Paragraph Proof Given: m1 + m2 = m4 Prove: m3 + m1 + m2 = 180° Paragraph Proof: It is given that m1 + m2 = m4. 3 and 4 are supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°. Holt Geometry 2-7 Flowchart and Paragraph Proofs Note 38 Holt Geometry 2-7 Flowchart and Paragraph Proofs Example 1B: Using the Converse of the Corresponding Angles Postulate Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 Holt Geometry 2-7 Flowchart and Paragraph Proofs Holt Geometry 2-7 Flowchart and Paragraph Proofs Example 2A: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. 4 8 4 8 4 and 8 are alternate exterior angles r || s Conv. Of Alt. Ext. s Thm. Holt Geometry 2-7 Flowchart and Paragraph Proofs Example 2B: Determining Whether Lines are Parallel Use the given information and the theorems you have learned to show that r || s. m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5 Holt Geometry 2-7 Flowchart and Paragraph Proofs Check It Out! Example 2b Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. m3 = 2x, m7 = (x + 50), x = 50 Holt Geometry 2-7 Flowchart and Paragraph Proofs Lesson Quiz: Part I Name the postulate or theorem that proves p || r. 1. 4 5 Conv. of Alt. Int. s Thm. 2. 2 7 Conv. of Alt. Ext. s Thm. 3. 3 7 Conv. of Corr. s Post. 4. 3 and 5 are supplementary. Conv. of Same-Side Int. s Thm. Holt Geometry