Topic: 5. 2. 2 parallel line determination [learning goals] 1, four methods of determining the parallel line for students and their initial use for simple reasoning. A preliminary study of simple reasoning and reasoning, understanding the need for geometric evidence and the rigour of the process of proof. The study focuses on the generalization of justice and the inference of the theorem, based on observational experiments. [scientific ready] triangle 1 filling out: a little outside of the line, parallel to this line. E [cooperative exploration] (i) parallel line determination method 1: chp d1, observation thinking: what does the triangle do? What's the relationship between ∠1 and ∠2? Ag2b2, decision method 1: application format: f. ∵∠ 1 = 2 (known) simply states: application of the ab∥cd (equal to the azimuth, parallel to two lines): what is the point of the carpentry master drawing parallel lines using an acetometer? (ii) parallel line methods of determination 2, 3 : 1, reflection: teaching materials 14 pages (tried to write the reasoning process) ∵∠2 = ∠3 (known) simply states: ∴b (equivalent internal angle, two lines parallel), change the last condition to ∠2 + ∠4 = 180°, can you get a ∥b? Method 3: application format: ∵∠2 + ∠4 = 180° (known): (iii) mathematical thinking: teaching materials 15 pages. Cp 34bc [increased feedback] 1 2 (i) pedagogical material 15 page 2 1a (ii) exercise: pedagogic material 15 page 1; 2 and 3a (iii) text sheet b (1) (2) method 1: if a ∥b, b∥c that is, both lines parallel the third line, and both lines parallel each other. Method 2: as in figure 1, if ∠1 = ∠3 a ∥c. Method 3: as figure 1, if. Method 4: as figure 1, if. Method 5: as figure 2, if a ⊥b, a⊥c, a ∥c. That is, within the same plane, two straight lines vertically in the same line parallel to each other. ° ° ∠ ∠ ∠ ∠ ∠ ∠ ∠ + + + + + + + + = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = , = ; , = = = = = = = = = = = = = = = = = = = = = = = b 3. Known ∠1 = ∠2, ac ∠ dab, test note dc∥ab. Dc2
