Reference answer
1. 1，b； Tip: Pay attention to the concept of translation. "The car skids on the ground when it brakes suddenly" belongs to translation.
2、B； Hint: According to the area relation, ab-bc-ac+c2 exists.
3、C； Prompt: ∵∠ 1=∠2,∴AB∥ED error.
4、A； Prompt: Prompt: According to the positional relationship of straight lines in the plane, there is "parallel or intersecting with A and B"
5、A； Hint: Figure A can be regarded as a translation of a part of the pattern itself, but none of the other patterns are.
6、C； Hint: 4× 2 = 8
7、B； Hint: According to the characteristics of translation
8、D； Prompt: "(1) and (2), (2) and (3), (1) and (4) are all translations" is incorrect.
9、D； Tip: Pay attention to the endpoint of the solution set.
10、D； Tip: If it is substituted for verification, it is easy to know that a= 1/4.
Second, 1 1, -2
12、0.2
13、∥; Tip: According to the complementation of internal angles on the same side, two straight lines are parallel.
14、 16,56; Tip: Please note that every time you add a straight line, you should explore the number of planes.
15, ∨ (inference of parallel axioms). According to the inference of parallel axiom, parallel relation can be transmitted.
16、22,30,0;
17, 2cm Tip: Every point on the map has been translated by 2cm.
18, not necessarily
19、80 ; Tip: The line segments corresponding to the translated figure are parallel and complementary according to the internal angles on the same side.
20. Right triangle; Tip: If two corners are redundant, then the other corner must be a right angle.
3. 2 1, (1) solution 3x+7-
X < 2。
The solution set of inequality group is -< x < 2.
The integers in -< x < 2 are-1, 0 and 1.
The integer solution of the inequality group is:–1, 0,1.
(2) ; Tip: Substitute x=68-y from (1) into (2) to get y = 23 and x = 45.
22. Proof: ∫ (known),
∴ (equivalent substitution)
∵
The complementary angles of equal angles are equal.
∴ (Internal dislocation angles are equal and two straight lines are parallel)
23. Solution: ∴.
∴, namely:
∴op∑AE(4 points), ∴
Once again: Ⅷ
Namely.
24. evidence: ∵AD⊥BC, EG⊥BC,
∴∠EGC=∠ADC=90，
∴AD//EG. ∴∠ 1=∠3,∠2=∠E，
∠∠e =∠3，∴∠ 1=∠2，∴AD ∠BAC。
25、( 1)28; (2)56 sheets; (3)45 species.
26. Analysis: Many students think that this problem can't be solved because they only know the length of the rectangle and don't know the length of other short sides after overlapping. In fact, this problem can be solved as long as students carefully observe and use the means of translation.
As shown in the figure, the short sides b and d translate downward, and the sum of their lengths is exactly the length of a rectangle; Short sides A and C are translated to the right, and the sum of their lengths is 9 meters. After translation, it can be found that the circumference of this figure is exactly four times the length of the original rectangle.
Solution: 9×4=36 (m). A: The circumference of this figure is 36 meters.
27.( 1) On the surface, the circumference of the figure on the right seems to be longer than that on the left. If you translate the relevant line segments in the right picture from the perspective of motion, you will find that the perimeters of these two figures are the same.
(2) Solution: The translated graph is shown in the above figure.
Comments: This question should select five key points: three vertices of triangle and two vertices below rectangle, and determine the position of the translated figure according to the direction and distance of translation.
28. analysis: suppose you can make x small boxes of type a and y small boxes of type b, which can be obtained according to the meaning of the question.
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