[Volume I]
First, multiple-choice questions (4 ′× 8)
1, the conclusion that two straight lines are not directly parallel is (c)
A, the internal dislocation angle is equal to b, the congruence angle is equal to c, the antipodal angle is equal to d, and the internal angles on the same side are complementary.
4. Given an inner angle 46 of a right triangle, the other inner angle is (c).
A, B, C, D, 54
5. As shown in the figure, if ∠ 1=∠2 is known, there is (b).
a、AB‖CD B、AE‖DF
C, AB‖CD, AE‖DF D are all wrong.
6. In the following statement, it is not certain that two straight lines are parallel (D? )
A. The internal dislocation angle is equal. Are two straight lines parallel? B. The same angle is equal and the two straight lines are parallel.
C the internal angles on the same side are equal, and the two straight lines are parallel. D in the same plane, two straight lines perpendicular to the same straight line are parallel.
Second, fill in the blanks (5 feet by 6 feet)
9. An equilateral triangle has _ _ _ symmetry axes.
10, in? In ABC, AB=AC,? A=60？ And then what? B=____ _，？ ABC is a triangle.
1 1. The two sides of a given isosceles triangle are 4 and 9 respectively, and its circumference is _ _ _ _ or _ _ _ _ _.
12. If the ratio of the three internal angles of a triangle is 3: 4: 7, then this _ _ _ _ is a triangle.
13, there are six thin sticks, their lengths are 2, 4, 6, 8, 10, 12 (unit: cm), and the three thin sticks that can be connected end to end to form a right triangle are _ _ _ _ _.
14. If the circumference of an isosceles triangle is 20, one side is 4, and the other two sides are _ _ _ or _ _ _ _.
Iii. Answer questions (8' is 13 and14; Questions 15 and 16 are 10')
15, as shown in the figure, a ∠ b, ∠ 1 = 122, ∠ 3 = 50, and find the degrees of ∠2 and ∠4.
Solution: 0
16, as shown in the figure, ad⊥bd ac⊥bc, AD = BC, so please judge? The shape of OAB
17, as shown in the figure, it is known that ∠4=∠B, ∠ 1=∠3, which proves that AC shares are ∠ bad.
Prove:
18, as shown in the figure, in △ABC, AD is the bisector of ∠CAB, DA=DB, DE⊥AB, AB=2AC.
Explain why △ACB is a right triangle.
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[Volume II]
First, multiple-choice questions (4 ′× 4)
19 As shown in the figure, under the following conditions, it cannot be judged that the straight line a‖b is ().
a、∠ 1=∠3 B、∠2=∠3
c、∠4=∠5 D、∠2+∠4= 180
20. As shown in the figure, there is a pumping station A at 32km northeast of the water tower O, and a straight water pipe is built between site B and AB at 24km southeast of the water tower, so the length of the water pipe is ().
A, 45km b, 40km c, 50km d, 56km.
2 1, as shown in the figure, the internal dislocation angle is ()
A. 10 to B.8 to C.6 to d.4.
22. As shown in the figure, in △ABC, ∠ ACB = 90, CD⊥AB in D, ∠ A = 30, then AD is equal to ().
a、4BD B、3BD C、2BD D、BD
Second, fill in the blanks (5 ′× 2)
23. The two sides of a right triangle are 3cm and 4cm respectively, so the length of the third side is _ _ _ _ _.
24. As shown in the figure, in △ABC, ∠ c = 90, AD bisects ∠BAC, BC= 10cm, BD=6cm, then the distance from point D to AB is _ _ _ _ _ _ _.
Third, the answer (8' is the 25th and 26th questions; Question 27: 10')
25. As shown in the figure, how many isosceles triangles can be drawn when one endpoint O of the line segment OD is on the straight line A, with OD as one side and the other vertex on the straight line A? (Use a ruler and compasses to find the corresponding isosceles triangle)
Solution: 2
26. According to the Regulations of the People's Republic of China on Road Traffic Management, the speed of a car on a city street should not exceed 70km/h, as shown in the figure, a car is driving on a straight road in a city street, and it just reaches 30 meters in front of the speedometer at a certain moment. Two seconds later, the distance between the car and the speed detector was 50 meters. Is this car speeding?
27. Think about this problem again according to the following origami methods:
Link AF, you know? What is AEF, a triangle? Please provide a justification for the answer.