1. Fill in the blanks (2 points for each small question, 38 points for * * *)

1. If the three sides of a triangle are 3, 7 and x, then the range of x is.

2. Choose three of the five line segments with the length of 1, 2, 3, 4 and 5 to form one.

; Triangle.

3. In △ABC, ∠ A: ∠ B: ∠ C = 3: 4: 5, then ∠A=, ∠B=.

4. Triangle is divided into right triangle, right triangle and right triangle according to angle. 5. As shown in figure 1, if AB⊥AC, AD⊥BC and ∠ 1 = 43, then ∠B=. 6. As shown in Figure 2, ∠ACE=∠BCE and BD=CD, then AD is a straight line of △ABC and CE is △ABC.

This line.

7. The midline, height and bisector of the triangle are all. 8. As shown in figure 1, there is a triangle with the height of AD. 9. As shown in Figure 3, it is known that there is an angle * * equal to ∠B in the figure if it is ⊿ABC, AC⊥BC, CD⊥AB and DE⊥AC. 10. As shown in Figure 4, it is known that ⊿ABC≌⊿ADE, d is a point on the bisector of ∠BAC, and ∠ BAC = 60, then ∠CAE=. 1 1. As shown in Figure 5, ⊿ABC≌⊿ADE, if ∠ B = 40, ∠ EAB = 80, ∠ C = 45, ∠EAC=,.

12. As shown in Figure 6, if AB=CD and AD=BC are known, then.

13. As shown in Figure 7, it is known that ∠ 1=∠2, AB⊥AC, BD⊥CD, AC and BD intersect at point E, then the congruent triangles in the figure is 14. When =, the equation will generate an augmentation. 15, the number whose square is equal to 16 is, and the cube root of-125 is. The square root of 16 is, the arithmetic square root of is, and the fifth square root is. Category name _ _ _ _ _ _ _ _ _ _ _ _17. If so, then x=. 18, all non-negative integers less than are. 19. Known. 20. known. 2 1. Known. 22. The cubic sum of two square roots of positive real number A is. 23. Among the following numbers, there are irrational numbers. 24. In, in, the value of x is. 25. If the equation has an increasing root, then the increasing root is _ _ _ _ _. 26. If the equation has no solution, it is in m = _ _ _ _ _ _ .27. △ABC, AB=AC, perimeter 16, and AB is 2 years longer than BC, then AC= BC= .28.E is a point in △ABC, and ∠A and ∠A∠B∠87 are ∠ B =. Multiple choice questions: (3 points for each small question, * * 15 points) 1. As shown in the figure, in ⊿ABC, CD⊥BC is on C and D is on the extension line of AB, then CD is ⊿ABC ().

A, the height of BC side, the height of AB side.

C, the AC side height d is incorrect. 2. The sum of any two acute angles in an acute triangle must be greater than (). a 120 b 1 10 c 100 D90 3。 It is known that the three internal angles ∠A∠B∠C of Δ Δ ABC satisfy the relation ∠ B+∠ C = Then this triangle () A must have an internal angle of 45. B must have an internal angle of 60. C must be a right triangle. D must be an obtuse triangle. 4. The following propositions are correct: () ① The sides corresponding to congruent triangles are equal; ② Three angles correspond to the coincidence of two equal triangles; ③ Three sides correspond to the coincidence of two triangles; (4) There are two triangles with equal sides. A. 4 B，3 C，2 D， 1。

5. As shown in the figure, it is known that AB=CD and AD=BC, then congruent triangles * * * in the figure has ().

A.2 For a fractional equation that can be reduced to a linear equation with one variable, if there is an increase in roots, then the following judgment is wrong: () A. The equation has only one increase in roots. B. the fractional equation has no solution. This equation has an added root that is different from the root. The increase of the root sign is substituted into the simplest common denominator. The simplest common denominator has a value of zero. 7. If the value of the score is 1, then X is equal to () A.-3b.3c.1D.–18.3.14159 is (). (1) Rational number (? (2) It is an infinite acyclic decimal; (3) it is an irrational number; The value of (4) is equal to 2.236. * * * There are () errors. 1 (b) 2 (c) 3 (d) 0 10。 In the following statements: (1) irrational number is an inexhaustible number; (2) Irrational numbers are infinite decimals; (3) Irrational numbers include positive irrational numbers, zero irrational numbers and negative irrational numbers; (4) Irrational numbers can be represented by points on the number axis. * * * Item () is correct. 1(b)2(c)3(d)4 1 1。 What is wrong in the following statement is that () (a) rational numbers can be represented by points on the number axis (b) all points on the number axis represent real numbers (c). The following statement is true: (). (a) 4 is the arithmetic square root of 8; (b) The square root of b)16 is 4; (c) It is the square root of 6; (d) There is no square root of 13; The following statement is incorrect: (). 14。 Then (). (a)-0.7(b)0.7(c)0.7(d)0.49 15。 If, then (). 7 16(b)76. 1(c)766555。 Then (). 17。 △ ABC, where AB=AC=4, BC=a, and the range of a is () AD=AE > 0b.0 < a < 4c.4 < a < 8d.0

1. As shown in the figure, find the degree of ∠ADB at the bisector of ⊿ABC, ∠ BAC = 60, ∠ B = 45, and AD is ⊿ABC. (10)

2. As shown in the figure, given AD=BC and AC=BD, can we draw the conclusion that ∠D=∠C? Tell me your reasons.

4. As shown in the figure, AC=BD, AD⊥AC, BD⊥BC, and verify that AD=BC. (6 points) 5. As shown in the figure, BF=CE, BC=EF, AB=DE, verify A = ∠ D.6, and solve the equation. 1), 2), 3), 4), 5), 6), 7. A group of students went to visit the campus. After they have walked for 30 minutes, the school will send an urgent notice to the team leader and send a student to start from the school by bike and catch up with the team by the same route. If the speed of cycling is twice that of the team, the distance from the school when students catch up with the team is 15 km. How long did it take the student from school to catch up with the team? 8. As shown in the figure, AD and AE are bisectors of △ABC, while ∠ B = 36, ∠ C = 76, so find the degree of ∠DAE. 9. In the activity of striving for a national sanitary city, a "youth commando" in our city decided to voluntarily remove a pile of garbage weighing100t. Residents nearby took the initiative to participate in voluntary labor, and the speed of garbage removal was doubled compared with the original plan. As a result, the task was completed four hours ahead of schedule. How many tons of garbage did the "Youth Commando" originally plan to remove every hour? 10, (10) A school restaurant plans to buy 12 dining table and some dining chairs. Now we know from two shopping malls, A and B, that each dining table of the same model is quoted in 200 yuan, and each dining chair is quoted in 50 yuan. A shopping mall said: each dining table is given a dining chair; According to the regulations of Mall B, all dining tables and chairs are sold at a 15% discount on the quoted price. So, under what circumstances is it more favorable to buy in mall A?