5. 2 parallel lines and their determination chapter v. Intersectional and parallel lines 5. 2. 2 determination of parallel lines 2 1. So far, what are the methods for determining the parallelity of two lines? (1) definition method: (this is not practical) (2) the reasoning of parallel justice: if a/b, b/c, a/c. (3) award method 1: equal azimuth, parallel to two straight lines. (4) award method 2: equal internal wrong angle, parallel to two straight lines. (5) award method 3: complementarity with inner angles, parallel to two straight lines. Importing new lessons. If yes, give your reasons. A b c 1 2 if ∠ 1 = ∠ 2, bc. If ∠ 1 = ∠ 2, then/... If ∠ = = =, then a/dc. C b b d 1 2 3 / / ad bc 2 3 pillow tracks the two tracks must be parallel when laying the tracks ... Think how to determine whether the two tracks are parallel? (3) if ∠d+dfe = 180°, which lines are parallel? Why? Example 1 as illustrated by e on ab, f on dc, g on bc extension. (1) if ∠b = ∠dcg, which two lines are parallel? Why? (2) if ∠d=dcg, which two lines are parallel? Why? A b d c e f g solution (1) ab c f/cd, with an equal angle and two parallel lines; (2) ad/bc, with an equal wrong angle, with two parallel lines; (3) ad/ef, with a complementary angle, with two parallel lines. Teaching new lessons. Example 2: as illustrated, ∠1=75o, ∠2 =105o ask: ab parallels cd? A c 1 4 2 3 b d 5 f e 75o 105o example 3 as ∠1 = ∠2 can judge ab∥df? Why ? ? ? ? F-c-a-b-e-1-2: can't... Add cedb's wrong angle equal, two lines parallel, if you can't judge ab-df, what do you think is the additional condition? Write this condition and explain your reasons. Think: in the same plane, two lines are vertically in the same line. Are the two lines parallel? B =, c⊥, c⊥, b?, c∴, c∴, c∴, c∴, c∴, c∴, b=, c⊥, c⊥, c⊥, c=, c=, b∥, c⊥, c⊥, c⊥, c⊥, c=, b=, c⊥, c⊥, b =, c?, b ⊥, b ⊥, c =, c ⊥, c =, c ⊥, c ∠, c ∠, c ∠, c ∠, b ∴, c ∴, b ∴, c ∴, b ∴, c ∴, c ∴, c ∴, c ∴, c ⊥, c ⊥, b ⊥, c=, b ⊥, c=, b ⊥, b ⊥, b ⊥, b ∵, b ∵, c ∵, b ⊥, b ∵, b ⊥, b ⊥, c =, b =, b =, b =, b +, b +, b +, b +, b = method 3: ∠5 =2 = 90° for the same plane, or 90° for the same vertical parallel line. If ∠1 = 120°, =3 = 3 = 180° for the same side angle, ∠2 = 90° for the two straight lines. Method 3: ∠5 = 90° for the same side angle, ∠1 =1 = 120°, 3 = 1 =1 = 180° for the side angle, abab/cd. () if a cd e 1 2 = 1 = 1 图1 = 1 = 1 图 2 = 1 e 2 = 2 ( 错 = 2 = = = = = = = = = argument: an internal wrong angle equals two lines parallel 3. One participant practices driving a car in the square, twice bending, moving in the same direction as before. These two turns may be () a. Turn right 50o for the first time, 130o b. Turn left for the second time, 30o left for the first time, 30o c. Turn right for the second time, 30o right for the second time, 50o left for the second time, 130o d. For the second turn left for the second time, 130o b 31 for the second time 1 ∵∠b+∠bcd = 180°, ∴ab∥cd; 2 =1 = ∠2, ∴ad∥bc; 3 ∵∠3 = ∠4, ∴ab∥cd; 4 ∵∠b = ∠5, ∴ab∥cd. ∴ access to ab∥cd is conditional on the following four conditions: 1 ∠b+ ∠bcd = 180°; 2 =1 =2; 3 =3 = ∠4; 4 ∠b = ∠5 in which the conditions for aluminum cd are determined to be () a. 1 b. 2 c. 3 d. 4 a b c d e 2 4 5 c 5. As shown, mf ⊥nf at point e, nf at point e, nf at point g, ∠1 = 140°, ∠2 = 50°, to test the location relationship between ab and cd, and to justify the reasons for it. Think extension 1 2 program 1: 40° 40° 90 120 150 180 60 30 gr e at. Protractor 0 10 20 50 40 30 60 70 80 90 110 110 120 130 140 150 160 170 180 10 20 40 50 70 80 100 110 110 130 130 160 160 160 160 170 170 170 90 180 60 60 60 90 120 150 60 30 g r e a t. Protractor 0 10 20 50 40 30 60 70 80 90 100 110 110 120 130 140 150 160 170 180 10 20 40 50 70 80 100 110 110 130 160 140 170 160 170 170 170 170 40 120 150 180 180 180 180 180 110 110 130 140 170 40 90 40 90 120 180 60 30 g r e at。protractor 0 10 20 50 40 30 60 70 80 90 110 110 120 130 140 150 160 170 180 10 20 40 50 70 80 100 110 110 130 130 160 160 160 160 170 170 170 90 180 60 60 60 90 120 150 60 30 g r e a t. Protractor 0 10 20 50 40 30 60 70 80 90 100 110 110 120 130 140 150 160 170 180 10 20 40 50 70 80 100 110 110 130 110 130 160 160 160 160 160 170 170 170 1 2 40° programme 2: 140° 40° 90 120 150 180 60 30 ge e at. Protractor 0 10 20 50 40 30 60 70 80 90 110 110 120 130 140 150 160 170 180 10 20 40 50 70 80 100 110 110 130 130 160 160 160 160 170 170 170 90 180 60 60 60 90 120 150 60 30 g r e a t. Protractor 0 10 20 50 40 30 60 70 90 110 120 130 140 150 160 170 180 10 20 40 70 70 80 80 80 80 80 80 80 80 80 80 100 2 programme 3: 1. Same angular angle, parallel to two straight lines, parallel to the inner angles 3. 3. 3. Parallel to the inner angles, parallel lines. 4. Parallel to the two straight lines, parallel to the straight lines. 6. Definition of parallel lines.
