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Judge whether the following propositions are true or false? If false, give counter examples; if true, give proof (1) An angle must be less than its complement (2) If two lines are parallel, the inner angles of the same side must not be equal
Let's say the angle is a right angle
Both false angles can be right angles
Judge the true and false of the following propositions, and give proof (if true, give proof, if false, give counter examples)
(1) If a ^ 2 = 3 under the root sign, then a = 3
(2) As shown in the figure, we know that be ⊥ ad, CF ⊥ ad, the perpendicular feet are points E and f respectively, and be = cf. then ad is the middle line of △ ABC
The first is a false proposition, a can be equal to - 3
What about the second one?
Are the following propositions true or false? If true, please give proof; if false, please give counter examples
(1) The sum of the remainder and complement of an acute angle is less than that of a horizontal angle
(2) The difference between the complement and the remainder of an acute angle is equal to a right angle
False proposition: for example: 1. The true proposition of degree proves that if the acute angle is a, then its complement angle is 180 degrees - A, and the other angles are 90 degrees - A, then (180 degrees - a) - (90 degrees - a) = 90 degrees. Therefore, it is a right angle
A counterexample is given to show that the proposition "if two angles complement each other, then the two angles are adjacent complements" is a false proposition
Quick search
The inner corner of the same side complements each other
They are not neighborhood complements
Ding Ding read a story book, the first day read 20 pages, the next day read the remaining 40%, this is not read and read the same number of pages, the story book a total of 20 pages
How many pages? Arithmetic
Set a total of X pages
Then 0.4 * (x-20) + 20 = 0.5x
So x = 120
If the set M = {0,1,2}, n = {x | x = 2A, a belongs to m}, then the set Mun=
It's filling in the blanks
M = {0,1,2}, the elements of set n are obtained by multiplying the elements in m by 2, so n = {0,2,4},
So Mun = {0,1,2,4}
Someone walks 6 kilometers per hour, and the speed of cycling is 13 kilometers per hour. How many times is the speed of cycling walking?
fast
It's 13 times 6 = 13 out of 6
What's the difference between galvanized sheet with zinc flower and galvanized sheet without zinc flower
Normal zinc flower (commonly known as ordinary zinc flower and large zinc flower) hot dip galvanized steel strip (plate) is the basic variety of hot dip galvanized steel strip (plate). It is a kind of coated plate with obvious zinc flower morphology formed by zinc grains growing freely in the normal solidification process after hot dip galvanizing under the condition of antimony or lead in zinc solution, Galvanized sheet with zinc flower and galvanized sheet without zinc flower are only appearance difference, no quality difference
[urgent] the highway between a and B is 375km long. A car and a bus start from a and B at the same time and run in opposite directions
The average speed is 90 / km / h, and the average speed of the bus is 60 km / h. how many hours after the two buses leave, do they meet on the way? (solution of linear equation with one variable)
The two vehicles meet on the way x hours after departure: (90 / km / H + 60 km / h) x = 375, x = 2.5 hours
Four unknowns and three equations
Known: a + B + C = 120; B + C + D = 95; a + C + D = 100;
Ask: a + B + C + D =?
A + B + D = 95 (1) a + B + C = 110 (2) a + C + D = 125 (3) B + C + D = 90 (4) (1) + (2) 2 (a + b) + C + D = 205 (5) (3) + (4) a + B + 2 (c + D) = 215 (6) (6) × 2 - (5) 3 (c + D) = 225C + D = 75 (7) (7) substitute (3) a = 125-75 = 50 (7) substitute (4) B = 90-75 = 15 substitute (1) d = 95-50-15 = 30C = 75-30 = 45
RELATED INFORMATIONS
- 1. If AB = 0, then a = 0 is a false proposition
- 2. A counterexample is given to show that the following proposition is a false proposition, [1] if a > b, then 1 / A
- 3. Please give a counter example to show that the following proposition is false 1. Equal angles are right angles 2, if a + B = 0, then a = 0, B = 0 3. If ∠ 1 is greater than ∠ 2, then ∠ 1 is an obtuse angle
- 4. If the real number a B satisfies a + B < 4, then a = 1 and B = 2 find its inverse proposition, no proposition, inverse no proposition, and its true and false
- 5. Write a proposition that the sum of two rational numbers is the inverse proposition of rational numbers. If the inverse proposition is not sure of the answer, don't mistake people!
- 6. Write down the inverse proposition of the following proposition, and judge the truth of the original proposition and the inverse proposition. (1) natural number must be rational number. (2) if | a | = | B | & _; then a = B (3) If a = B, then a ^ 3 = B ^ 3
- 7. For any rational number x, x-3 + X-6, is there the smallest absolute value? Why For any rational number x, x-3 + X-6, is there the smallest absolute value and why
- 8. What is the square of rational number 2?
- 9. Let a and B be rational numbers. Judge whether the following statements are correct and explain the reasons ① If a = - B, then | a | = | B| ② If | a | = | B |, then a = - B
- 10. The equivalent proposition to the proposition "if a ∈ m, then B ∉ m" is () A. . if & nbsp; a ∉ m, then & nbsp; B ∉ MB. If B ∉ m, then & nbsp; a ∈ MC. If & nbsp; a ∉ m, then & nbsp; B ∈ MD. if B ∈ m, then & nbsp; a ∉ M
- 11. Give counter examples to prove that the following propositions are false propositions (1) if a > b, then 1 / A
- 12. The counter example is used to show that the proposition "if M > 1, then x ^ 2-2x + M = 0 has real root" is a false proposition
- 13. Judge whether the following propositions are true or false. If they are true, please give proof. If they are false, please give counter examples 1. If the two sides of a corner are parallel to the two sides of the other corner, then the two corners are equal 2. Two triangles of equal area are congruent triangles 3. The sum of the distances from any point in the equilateral triangle to the three sides of the triangle is equal to the height of the equilateral triangle 4. There are two congruent triangles with equal heights on both sides and one of them 5. There are two congruent triangles whose heights on the two sides and the third side correspond to the same
- 14. To judge a proposition, if a > 0, then the bisection of a > the true or false of A. if it is a true proposition, please prove it. If it is a false proposition, please give a counter example
- 15. Judge the truth of the negation of proposition p: the square of (- 2) under the root sign = 2 Judge the truth of the negation of proposition p: the square of (- 2) under the root = - 2 The title was copied wrong just now sorry
- 16. Given the condition P: | x + 1 | > 2 and the condition Q: 5x-6 is greater than the square of X, what is the condition of its no proposition
- 17. It is known that: P = a square + 3AB + b square, q = a square-3ab + b square, and P - [q-2p - (- P-Q)] + r = a square + 2Ab + b square
- 18. Given proposition p: x > 0, proposition q: x square > 0, then p is a, B and C of Q, and a + b > C is a, B and V Given the proposition p: x > 0 and the proposition q: x square > 0, then p is Q a. If B and C are three line segments, then a + b > C is that a, B and V can form a triangle Li Min is an 18-year-old college student
- 19. It is known that a, B and C are nonzero rational numbers It is known that a, B and C are nonzero rational numbers The molecules are a + B + C + BC + AC + AB + ABC. These are molecules; The denominator is the absolute value of the numerator above Simplify them. The sign is the plus sign By 9:30 tonight, urgent! Before 10:00 The process should be clear and easy to understand!
- 20. If the rational numbers a and B satisfy | ab-2 | + | 1-B | = 0, Let's try to find one of ab ＋ (a ＋ 1) (B ＋ 1) ＋ (a ＋ 2) (B ＋ 2) ＋ ＋﹙a＋2011）﹙b＋2011 A value of 1 / 2