(Total score: 120, test time: 60 minutes)
First, multiple-choice questions (3 points for each small question, ***24 points)
1, in the following groups, can form a right triangle is ().
A: 4,5,6 b: 1, 1 c: 6,8, 1 1 d: 5,12,23.
2. if ∠ c = 90, a = 12 and b = 16 in rt △ ABC, the length of c is ().
A: 26 B: 18 C: 20 D: 2 1
3. The triangle () is obtained after all sides of the right triangle are reduced or expanded by the same multiple.
A. It may be an acute triangle B. It may not be a right triangle C. It may be a right triangle D. It may be an obtuse triangle.
4. The opposite sides of ∠A, ∠B and ∠C in △ ABC are A, B, C, AB = 8, BC = 15 and CA = 17 respectively, so the following conclusion is incorrect ().
A: △ ABC is a right triangle AC is the hypotenuse B: △ ABC is a right triangle ∠ ABC = 90.
C: the area of △ ABC is 60 d: △ ABC is a right triangle, and ∠ A = 60.
5. If the length of an equilateral triangle is 2, the area of the triangle is ().
A: B: C: D:3
6. As we all know, A, B and C are the lengths of three sides of a triangle. If they are all satisfied, the shape of the triangle is ().
A: isosceles triangle with unequal base and side B: equilateral triangle C: obtuse triangle D: right triangle
7. One ship sailed northeast from Port A at a speed of 16 knots, and the other ship sailed southeast from Port A at a speed of 12 knots. After leaving the port for 3 hours, the distance between the two ships is ().
A: 36 nautical miles B: 48 nautical miles C: 60 nautical miles D: 84 nautical miles
8. If the medium, medium and high AD= 12, the length of BC is ().
A: 14b: 4c: 14 or 4 D: None of the above is true.
Fill in the blanks (3 points for each small question, 24 points for * * *)
9. The carpenter wants to make a rectangular desktop, which is 80cm long, 60cm wide and diagonal 100cm. Then this desktop (fill in "qualified" or "unqualified");
10. As shown in the figure, three sides of the right triangle ABC are square outward, and their areas are, and;
1 1. Put the ladder with a length of 10 meter against the wall. If the upper end of the ladder reaches the bottom end of the ladder,
If the distance is 6 meters, then the distance from the bottom of the ladder to the bottom of the wall is meters.
12, as shown in figure,, then ad =；;
13. If all three sides of a triangle are satisfied, the largest angle in the triangle is:
14. It is known that the two right-angled sides of a right-angled triangle are 6cm and 8cm respectively, so the height on the hypotenuse of this right-angled triangle is;
15, write a set of all even pythagorean numbers;
16. As shown in the figure, it is known that a bamboo pole with a length of 8m was broken at 3m from the ground, and the top of the bamboo pole was against the ground. At this time,
The top is m from the bottom;
Third, answer questions.
17, (4 points) As shown in the figure, the AC for tunnel construction for railway is measured ∠ A = 40 ∠ B = 50, AB = 5 km, BC = 4 km. If the tunnel is 0.3 km per day, how many days will it take to dig the AB tunnel?
18, (4 o'clock) at △ABC, ∠ c = 90. (1) Given c=25 and b= 15, find a; (2) Given a =, ∠ A = 60, find b and c. 。
19, (4 points) as shown in the figure, there is a path through the rectangular grassland ABCD, if AB = 60m, BC = 84m, AE = 100m,
What is the area of this path?
20.(6 points) As shown in the figure, it is known that in △ABC, CD⊥AB is in D, AC = 20, BC = 15 and DB = 9.
(1) Find the length of DC. (2) Find the length of AB.
2 1.(4 points) As shown in the figure, the ladder AB leans against the wall, the distance from the bottom of the ladder A to the wall root O is 3m, and the top of the ladder A moves outward to A', so that the distance from the bottom of the ladder A' to the wall root O is 4m, while the top of the ladder B descends to B', thus finding the length of BB' (the length of the ladder AB is 5 m).
22.(6 points) The length, width and height of the box are 4m, 3m and12m respectively. What is the longest stick that can be put in the box? (Draw a schematic diagram and solve it)
23.(4 points) As shown in the figure, Xiaohong origami with a rectangular piece of paper ABCD. It is known that the width of paper AB is 8cm, and the length of paper BC is10cm ... When Xiaohong is folded, the vertex D falls at point F on the side of BC (the crease is AE). Think about it, how long is EC at this time?
24.(8 points) Carefully observe the pictures, carefully analyze all kinds, and then answer the questions:
+1=2 = (1) where n(n is
+1=3 = a positive integer) represents the above change law;
+1=4 = (2) Calculate the length of O;
(3) Find the value of++…+.
25.(4 points) Given that the perimeter of a right triangle is 2+ and the hypotenuse is 2, find its area.