At most, there is a counter-proof that the angle is a right angleWhen using reduction to absurdity to prove that "at most one angle is a right angle," one first had to raise the proposition that "at most one angle is a right angle," and then set the anti-proposition that "at most two or three angles are right angles."(Since the original proposition indicated that the number of right angles was at most one, then the contradiction was that the number of right angles was two or three). Next, he deduced according to the rules of reasoning to prove the falsehood of the counter-proposition. Finally, according to the Law of Excluded Middle, since the opposite proposition was false, the original proposition that "at most one angle is a right angle" was true.
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Reverse Right-angle TeachingHere are some key points about teaching the reverse right angle:
1. [Familiar with the road conditions: First of all, you need to know the right angle of the road conditions, such as the width of the road. This is the basis for the reverse right angle operation.]
2. ** Speed Control **: Before entering the reverse angle, the speed must be slow. If the speed is too fast, you can slightly apply the foot brake, but you can't step on it to prevent the car from stopping and causing it to fail.
3. ** Vehicle position **: Before the car enters the reverse angle, it should be close to the other side of the curve. For example, when making a right turn, the car should be close to the left side of the lane, and at the same time, it should not be pressed to the left side line.
4. ** Turning timing **: When the car slowly enters the anti-right angle area, look at the corresponding steering mirror (for example, look at the right mirror when turning right). When the mirror has just passed the anti-right angle line by a certain distance (2 - 75px), quickly turn the steering wheel in the corresponding direction (for example, turn right, turn right). When the corresponding tire (for example, turn right, turn right) has passed the anti-right angle, start to turn the steering wheel and look ahead.
There were also some techniques:
1. When the car body is close to the outer right-angle line, for example, when the middle of the left and right front door triangular window is aligned with the inner and outer right-angle line, the direction of the corresponding direction (left or right) will be hit to the end, and the car timing will return to the right.
2. When you pass the first gear, don't step on the accelerator; when you turn at a right angle, try to stick close to the corresponding sideline (if you turn right, stick close to the right sideline); when a specific part of the cab (such as the seat belt part) passes the corner, you have to turn in the corresponding direction (if you turn left, turn left) until you hit the end; when you see the front of the car facing the exit, quickly turn the direction to prepare for the next operation.
3. When driving into the examination hall, try to stick close to the corresponding curb (such as the right side of the road to the right); once the front of the curb is blocked by the hood, you have to turn in the corresponding direction (such as the left turn to the left) until the end; when you see the front of the car facing the exit, you quickly turn the direction back.
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There cannot be two right angles in a triangle1. First, he reversed the assumption:
- Assuming that there are two right angles among the three internal angles of the triangle, A, B, and C, let's set A = B=90^{\circ}.
2. Then, he came up with a contradiction:
- At this time, the sum of the internal angles of the triangle is [A + B + C=90^{\circ}+90 ^{\circ}+C = 180^{\circ}+C], because [C'gt0 ^{\circ}], so [A + B + C'gt180 ^{\circ}], which contradicts the sum of the internal angles of the triangle is [180^{\circ}], so [A = B = 90^{\circ}] is not true.
3. In the end, he came to a conclusion.
- Therefore, there could not be two right angles in a triangle.
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Can inverse trigonography only represent positive angles? Right? Right?No, the inverse trigonometer could not only represent the positive angle. The range of the inverse trigonometrigram function covered a certain range of positive and negative values, depending on its domain and the properties of the function itself. For example, the range of the arcsin function was [-Pi/2, Pi/2], which included both positive and negative angles; the range of the arccosine function was [0, Pi], which meant that the inverse trigonometric-function could not only represent positive angles; and the range of the arctan function was (-Pi/2, Pi/2), which included positive and negative angles. Therefore, the inverse trigonometer function could represent positive and negative angles and many other situations.
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How to turn the steering wheel at a right angleThere were several ways to turn the steering wheel when making a right angle turn. According to the document [1], when the right mirror was parallel to the right angle, the steering wheel could be turned two times to the right and two times to the left. The document [2] mentioned that it was possible to determine when to turn the steering wheel based on the position of the front of the car and the corner. When the front of the car was about to reach the opposite side of the line or felt that its position was equal to the corner, it was necessary to immediately turn the steering wheel in the direction of the turn. It was also mentioned in document [4] that if you turn left at a right angle, turn the steering wheel 1.3-1.5 times to the left, and if you turn right at a right angle, turn the steering wheel 1.3-1.5 times to the right. In summary, when turning a right angle, you can judge when to turn the steering wheel according to the position of the front of the car and the corner. Generally, you need to turn the steering wheel a full number of times to complete the turn.
Reflection on teaching plan of inclination angle and slope of a straight lineThe following are some of the main points of teaching reflection on the angle of inclination and slope of a straight line:
** 1. Success **
1. ** Introduction and transition of knowledge **
- When introducing the concept of inclination angle, it could be introduced by saying," Two points determine a straight line. After removing a point, countless straight lines can be made. The difference between these straight lines is the degree of inclination." This could naturally guide students to think about the concept of inclination angle.
- It was reasonable to introduce the concept of straight line slope with the help of the concepts of slope angle, slope and the relationship between them learned in junior high school. It could help students transition from familiar knowledge to new knowledge.
- From the idea of " two points determine a straight line, the straight line determines the inclination angle, and if the slope exists, the slope is also determined. Can the slope be calculated by any two points on the straight line?", he introduced the slope calculation formula, and set up exercises to let students discover the relationship on their own, which was helpful for the construction of knowledge.
2. ** Details **
- Pay attention to the connection between old and new knowledge, such as the concept of tilt angle and slope, and the knowledge learned before.
- For a straight line with a slope of 90°, there was no such error-prone point. It could be understood by students from the essential point of view of the non-existence of the diagonal value, rather than simply a rule. When the slope exists, the relationship between the positive and negative of the slope and the range of the inclination angle is also analyzed in detail and displayed directly, which can deepen the students 'understanding of the concept.
- The exercises were set according to the students 'cognitive rules, from special to ordinary, from shallow to deep.
3. ** Infiltrating the way of thinking **
- In the whole teaching process, through the combination of numbers and shapes, students can better understand the concept of inclination angle, slope and the situation where the slope does not exist when the inclination angle is 90°, so that the abstract concept becomes intuitive and easy to understand.
4. ** Overall control of the classroom **
- Focus on summary, interact with students, pay attention to students 'learning status, and help students consolidate their knowledge.
- He was good at using multimedia-assisted teaching, and his teaching posture was natural and generous. His Mandarin was standard, and he could give students a good learning experience.
** 2. Inadequacies **
1. ** Teaching experience **
- The lack of experience caused him to be too nervous in public classes or the first class, repeating the knowledge points too many times, and the time arrangement was unreasonable. For example, he spent too much time on " the existence of slope and the discussion of the positive and negative slope and the value range of the slope angle." This caused the deduction of the slope formula and the explanation of the examples to be insufficient, and even dragged on the class. Moreover, the content of the course was not finished, and the difficult points could not be highlighted and broken through.
2. ** In terms of students 'main body status **
- When emphasizing the key knowledge, the speed was too fast and the number of repetitions was too many, which did not give the students enough space to think and play. For example, in the discussion of the non-existence of the slope of a straight line with an inclination angle of 90°.
- They did not pay enough attention to the individual students and did not take into account the learning needs of different students.
3. ** Introduction to class **
- Inappropriate classroom introductions would affect the teaching effect. For example, if the students simply introduced questions or paid too much attention to Descartes 'introduction method, if they did not combine the actual situation of the students with the overall grasp of the course content, it would make the students feel lost or not interested, and it might also lead to a smooth connection in the teaching process.
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