2. As shown in the figure, it is known that AB=CD, DE⊥AC, BF⊥AC, E and F are vertical rulers, and DE=BF.
Proof: AE=CF, AB∨CD. English and French
A b
3. It is known that ABC and ADE are isosceles right triangles with common vertices.
Proof: (1)BD=CE, (2)∠ 1=∠2.
E
D
A
C
B
4. Known: as shown in the figure, AB⊥BD, ED⊥BD, AB=CD, BC = DE A.
Verification: AC ⊥ CE E.
A C D
5. As shown in the figure, m is ABC, a point on the side of BECF BC, and be = cf
Proof: AM is the center line of ABC. A
F
B M C
E
6. Know: As shown in the figure, ∠BAC=∠DAE, ∠ABD=∠ACE, AB=AC.
Verification: BD=CE.
A
E
D
B.C.
7. There are (339) natural numbers less than 400 without the number 8.
8. Nine copper coins, one of which is fake, the authenticity is only different in quality. If you weigh it at least (8 times) with a balance without weight, you can definitely find out the fake copper coins.
9. There is a warehouse ***5 warehouses every100km on the highway. Warehouse 1 has 10 tons, warehouse 2 has 20 tons, warehouse 5 has 40 tons, and the other two warehouses are empty. Now I want to put all the goods in one warehouse. If the freight of 1 km per ton of goods needs 1 yuan, then it needs at least (10000) yuan.
1No. 100 km 2 100 km 3 100 km 4 100 km 5.
10 tons, 20 tons and 40 tons
10. Grade 6 * * *, 207 students, 2/1boys and 7 girls were selected to take part in the math competition. The remaining students are half male and half female, and there are 97 girls in grade 6.
1 1. Xiaolan and Xiaoli play a guessing game. Xiaolan writes a four-digit decimal on the straight line for Xiaoli to guess. Xiaoli asked, "Is it 603 1?" Xiaolan said: "I guessed a number, and the location is correct." Xiaoli asked again, "Is it 5672?" Xiaolan said: "I guessed both numbers correctly, and neither position is right." Xiaoli asked again, "Is it 4796?" Xiaolan said, "I guessed four numbers right, but none of them are right." Can you infer the four digits written by Xiaolan from the above information? 6974
12. If 20 rabbits can be exchanged for 2 sheep, 8 sheep can be exchanged for 2 pigs, and 8 pigs can be exchanged for 2 cows, how many rabbits can 4 cows be exchanged? 640
13. Light light blue is 8 years old this year and her father is 38 years old. How old is light light blue? Dad is exactly four times as old as light light blue. 10
14. For the people, every three empty soda bottles can be replaced by 1 bottle. Light light blue bought 99 bottles of soda in the summer vacation, and changed them into empty bottles after drinking them. How many bottles of soda can she drink at most? 147
15. In a division formula, the sum of dividend, divisor, quotient and remainder is 75, the known quotient is 8, and the remainder is 2. What are the dividend and divisor?
58 7
16. There are two iron wires of the same length. The first one is minus 30cm, the second one is minus18cm, and the second one is twice as long as the first one. How many centimeters is left in the second wire? 24
17, there are 1, 2, 3, 4, 5, 6, 7, 8 and 9 cards, each with three cards. A said, "The product of my three cards is 48", and B said, "The sum of my three cards is 15".
238 564 179
/kloc-how many different rectangles can a 0/8.24cm long wire enclose (the length and width are all whole centimeters, not counting joints)? What are the areas? Compare it again. What can you find? six
19 Master Zhang is used to taking two days off every five days of work. Recently received the task of producing 330 parts. He produces 30 parts every day. How many days will it take to complete this task?