Converse proposition converse theorem

Converse proposition converse theorem

Converse proposition
Generally defined, in mathematics, we call statements that can be judged true or false by language, symbol or formula as propositions
For two propositions, if the condition and conclusion of one proposition are the conclusion and condition of another proposition respectively, then the two propositions are called reciprocal propositions, one of which is called the original proposition, and the other is called the inverse proposition of the original proposition
Original proposition: for example: the same position angle is equal, two straight lines are parallel
Converse proposition: for example: two straight lines are parallel and the same angle is equal
nature
If the original proposition is true, its inverse proposition is not necessarily true
If a = 0, then AB = 0 is true
Inverse proposition: if AB = 0, then a = 0 is false
relationship
Mutual relations: the original proposition and the inverse proposition are opposite to each other, the inverse proposition and the inverse proposition are opposite to each other, the inverse proposition and the inverse proposition are opposite to each other, the no proposition and the original proposition are opposite to each other, the original proposition and the inverse proposition are opposite to each other, and the inverse proposition and the inverse proposition are opposite to each other
True false relation: two propositions are reciprocal propositions or reciprocal propositions, and their authenticity is not related
Reciprocal proposition
In the four forms of propositions, the original proposition and the inverse proposition, the no proposition and the inverse no proposition are two pairs of reciprocal propositions
For example, "if event a is true, event B is also true."
Then its converse proposition is "if event B is true, then event a is also true."
Of course, we can't judge the truth of the inverse proposition by the truth of the original proposition
Inverse theorem
Inverse theorem in Science
If the converse proposition of a theorem can be proved to be true, then it is called the converse theorem of the original theorem. In this case, the two theorems are called the reciprocal theorem
For example: "in a triangle, if two sides are equal, their corresponding angles are also equal." its inverse theorem is: "in a triangle, if two angles are equal, their corresponding sides are also equal."
Inverse theorem in life
For example, the busier you are, the more things you have to do. The more idle you are, the less things you have to do. For example, the more outstanding your performance is, the easier it should be to rise, but the opposite is true. Or, the more you give, the more you lose

Converse proposition and converse theorem
It is known that "P is a point in the isosceles triangle ABC, if the distance from P to the three sides is equal, then PA = Pb = PC",
Prove this proposition, write its inverse proposition, and explain whether the inverse proposition is true? If so, please write the proof process
Wrong writing, we should change isosceles triangle to equilateral triangle

It's so simple. I'll take it
Because the distances to the three sides are equal. You first prove the bisector of P at the three corners of the triangle in pairs. Then it holds
If PA equals Pb and PC, then point P is on the bisector of the three corners of the triangle
It's true. It's OK to prove it!

The 2222 power of 1111 is higher than the 1111 power of 2222

1111 is larger to the power of 2222

There are 42 students in the sixth grade interest group, 47 of whom are boys. Later, there are several girls. At this time, the ratio of boys to girls is 6:5. How many girls are there in this interest group now?

6 + 5 = 1142 × 47 ﹣ 611 × 511 = 24 ﹣ 611 × 511 = 44 × 511 = 20 (people) a: now there are 20 girls in this interest group

Approximate number and significant number
52kg, accurate to 10kg, result -- accurate to 1kg, result -- accurate to 0.1kg, result——
The fourth power of 4.733 * 10 (accurate to thousands)

52kg, accurate to 10kg, 40kg, accurate to 1kg, 40kg, accurate to 0.1kg, accurate to 39.5kg
The fourth power of 4.733 * 10 (accurate to thousands) = the fourth power of 4.7 * 10

Wang Ming read a story book. On the first day, he read 40 pages, and on the second day, he read the remaining 1 / 3. At this time, the remaining pages are exactly the same as the pages he has read. How many pages are there in this book

Suppose the book has x pages
40+（x-40）/3=x/2
The solution is x = 160
The book has 160 pages

Given the set a = {a + 2, (a + 1) quadratic, a quadratic + 3A + 3}, if 1 is contained in a, find the value of real number A. who will teach me

A contains 1, then, a + 2, (a + 1), a + 3A + 3. At least one of the three values is 1. If a + 2 = 1, then a = - 1, if (a + 1) = 1, then a = 0, or a = - 2, if a + 3A + 3 = 1, that is, (a + 2) (a + 1) = 0, then a = - 2, or a = - 1

In a street, a cyclist and a pedestrian walk in the same direction. The speed of the cyclist is three times that of the pedestrian. Every 10 minutes, a bus overtakes the pedestrian, and every 20 minutes, a bus overtakes the cyclist. If a bus leaves at the same time from the departure station, how many minutes does it leave?

Suppose the interval of each bus is 1, then according to the meaning of the question, the speed difference between the bus and the pedestrian is: 1 △ 10 = 110, the speed difference between the bus and the cyclist is: 1 △ 20 = 120, because the speed of the cyclist is three times that of the pedestrian, so the speed of the pedestrian is: (110-120) △ 2 = 140, then the bus

How to calculate the area of galvanized steel duct?

Generally speaking, it is section perimeter * duct length * loss coefficient
1. Let the long side of the cross section of the rectangular duct be a, the short side be B, and the length be L
Area of rectangular duct = (a + b) * 2 * L * loss coefficient flange and loss coefficient are generally 1.1.2
2. Let the cross section diameter of circular duct be D and the length be L
Circular duct area = 3.14 * D * L * loss coefficient, flange and loss coefficient are generally 1.1.2

What is the proportion of the time taken by buses and cars to complete the whole journey

A certain distance, time and speed are inversely proportional