Eight grades first volume mathematics unit 123 examination paper four answers.

2009-20 10 school year first semester eighth grade mathematics unit examination paper.

Unit 1 Pythagorean Theorem

First, multiple choice questions

1. Given an RT delta, the two sides are 3 and 4 respectively, and the square of the third side length is ().

A.25 B. 14

C.7 D.7 or 25

2. In the following groups, triangles with side lengths A, B and C are not Rt△ ().

a=7，b=24，c=25

C.a=6，b=8，c= 10 D.a=3，b=4，c=5

3. If line segments A, B and C form Rt△, their ratio can be ().

A.2∶3∶4

C.5∶ 12∶ 13 D.4∶6∶7

4. It is known that one ship sails northeast from Port A at a speed of 16 knots, and another ship sails southeast from Port A at a speed of 12 knots. After leaving the port for 2 hours, the distance between the two ships is ().

25 nautical miles 30 nautical miles 35 nautical miles 40 nautical miles

5. As shown in the figure, if the side length of a small square is 1, the △ABC in the square grid is ().

A. Right triangle

B. acute triangle

C. obtuse triangle

D. None of the above answers are correct.

6. If the two right angles of Rt△ are N2- 1, 2n (where n >；; 1), then its hypotenuse length is ()

A.2n B.n+ 1

C.n2- 1 D.n2+ 1

7. It is known that ∠ c = 90 in Rt△ABC. If a+b= 14cm and c= 10cm, the area of Rt△ABC is ().

A.24cm2 B.36cm2

C.48cm2 D.60cm2

8. The base length of an isosceles triangle is 10 cm and the waist length is 13, so the area of this triangle is ().

40 to 50

C.60 D.70

9. If the three sides of a triangle are (a+b)2=c2+2ab, then the triangle is ().

A. equilateral triangle; B. obtuse triangle;

C. right triangle; D. acute triangle

10.

Map number 10

As shown in the figure, in the rectangular ABCD, AB=3 and AD=9. If the rectangle is folded so that point B coincides with point D and the crease is EF, the area of △ABE is ().

A.6 B.8

c 10d 12

Second, fill in the blanks

1 1. In Rt△ABC, ∠ c = 90; (1) if a=5, b= 12, then C = _ _ _ _ _ _ _ _ _ _ _ _ _； (2) if a= 15 and c=25, then b = _ _ _ _ _ _ ③ If c=6 1 and b=60, then a = _ _ _ _ _ _ ④ If a: b = 3: 4, c.

12. In △ABC, AC= 17 cm, BC= 10 cm, AB=9 cm, which is a _ _ _ _ _ _ _ triangle (divided by the angle).

13. The lengths of two right angles of a right triangle are 5 and 12 respectively, so the height on the hypotenuse is _ _ _ _ _ _ _.

14. On the calm lake surface, there is a red lotus, which is 1 m higher than the water surface. A gust of wind blew, and the red-violet was blown aside, and the flowers were flush with the water. It is known that the horizontal distance of red-violet is 2m, and the water depth here is _ _ _ _ _ _.

15. It is known that the lengths of two shorter line segments are 5cm and 12cm respectively. When the length of the longer line segment is _ _ _ _ _ _ _ _ cm, these three line segments can form a right triangle.

Third, answer questions.

16. The ratio of three sides of a triangle is 5:12:13, and the circumference is 60 cm. Find its area.

17. In response to the call of the central government to build a new socialist countryside, a town decided to build a local product processing base at point E between Station A and bilibili, which is 25 kilometers away from the highway. As shown in the figure, DA⊥AB is in A, CB⊥AB is in B, and DA= 15km and CB= 10km are known.

Map number 17

18. Xiaoming wants to know the height of the flagpole in the school. He found that the rope at the top of the flagpole hung 1 meter to the ground. When he pulled the lower end of the rope away for 5 meters, he found that the lower end just hit the ground to find the height of the flagpole.

19. One car leaves a city at the speed of 16 km/h and drives southeast, while another car leaves a city at the same time and place at the speed of 12 km/h and drives southwest. How far are they after leaving the city for 3 hours?

20. As shown in the figure, there is a cuboid whose length, width and height are 6, 4 and 4 respectively. There is an ant at the bottom A. What is the shortest distance it needs to crawl to eat the food at the top B of the cuboid?

2 1. As shown in the figure, it is known that in ABC, CD AB is in D D, AC=4, BC=3, BD= 3, BD=

(1) Find the length of CD;

(2) Find the length of AD;

(3) Find the length of AB;

(4) ABC is a right triangle

22. As shown in the figure, fold the rectangular paper ABCD in half, first fold the diagonal BD, and then fold it in half to make the AD edge coincide with BD to get the crease DG. If AB=8. BC=6, find the length of AG.

23. As shown in the figure, in the quadrilateral ABCD, AB=BC=2, CD=3, AD= 1, ∠ABC=900, try to find ∠ A times.

Reference answer

First, multiple choice questions

1.D 2。 B 3。 C 4 explosive D 5。 A six. D 7。 An eight. C 9。 C 10。 A

Second, fill in the blanks

11.132012412. Oblique angle13.14.1.515.

Third, answer questions.

16. Answer: The lengths of the three sides of a triangle are:

60× = 10/0cm 60× = 24cm 60× = 26cm

∵ 102+242=676=262

This triangle is a right triangle.

∴ s = × 10× 24 = 120cm2

17, solution: let AE= x km, then Be = (25-x) km,

In Rt△DAE, da2+ae2 = de2.

In Rt△EBC, be2+bc2 = ce2.

CE = DE

∴ DA2+AE2 = BE2+BC2

∴ 152+x2 = 102+(25-x)2

Solution: x= 10 km ∴ The base should be built at the distance from Station A 10 km.

18, solution: let the height of the flagpole be x meters, and the length of the known rope be (x+ 1) meters. According to Pythagorean theorem, we can get:

x2+52=(x+ 1)2

Solution: x= 12

Therefore, the height of the flagpole is12m.

19, 60km

20、AB= 13

2 1、( 1) (2) (3)5

22、AG=3

23. solution: AC, at Rt△ABC, AB=AC=2.

∴ ∠BAC=450，AC2=AB2+BC2=22+22=8

In delta △DAC, AD= 1 and DC=3.

∴ AD2+AC2=8+ 12=9=32=CD2

∴ ∠DAC=900