1, and the positional relationship between the two straight lines is ()
A, intersection, vertical b, intersection, parallel c, vertical, parallel d, intersection, vertical, parallel
2, as shown in the figure, is a "seven" shape, and ∠ 1 is ().
a、2 B、3 C、4 D、5
3. Draw parallel lines of known straight line A through point A, and you can draw ().
A, 0, b, 1, c, 2, d, indefinite
4. In the plane rectangular coordinate system, the position of point P (- 1, 2) is ().
A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant
5. Given that the distance from point P on the Y axis to the origin is 5, the coordinate of point P is ().
A, (5,0 0) b, (0,5) or (0,5 5) c, (0,5 5) d, (5,0) or (-5,0).
6. In the following figures, the one that correctly draws the high BD on the AC side is ().
7. As shown in the figure, ∠ 1=∠2, ∠ 3 = ∠ 4 and ∠ A = 80, then ∠BOC is equal to ().
A, 95 b, 120 c, 130 d, uncertain.
8, the following graphics, unstable is ()
Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question and 24 points for * * *).
9. As shown in the figure, line A and line B intersect, and it is known that ∠ 1 = 38, then ∠2= degree, ∠ 3 = degree, ∠ 4 = degree.
10, as shown in the figure, it is planned to divert the river into the pool A, first divert AB⊥CD, and then ditch along AB, which can make the river channel shortest. This design is based on:
1 1, given a straight line A∑B, the distance from point M to straight line A is 4cm, and the distance from straight line B is 2cm, so the distance from straight line A to straight line B is:
12. As shown in the figure, translate the right-angled trapezoid ABCD to the right-angled trapezoid EFGH along the AD direction. It is known that HG=24cm, MG=8cm and MC=6cm, then the area of the shadow part is;
13. Point P is in the third quadrant, and the product of abscissa and ordinate is 12. Write the coordinates p of three qualified points:
、 、 ;
14, there is an English word whose alphabetical order corresponds to the ordered number pairs as shown in the figure.
(5,2),(2,2),(7,2),(5, 1),
Please write down this English word or translate it into Chinese.
15. Starting from a vertex of nonagon, you can draw a diagonal line.
They divided nonagon into triangles,
The sum of the internal angles of these triangles and the internal angles of the octagon (fill in ">" or "
16, as shown in the figure, there is an isosceles triangular piece of paper with a bottom angle of 35. First, it passes a little above the bottom edge.
Cut along the direction perpendicular to the bottom edge and divide it into two parts: a three-step and a quadrilateral.
Then in the quadrilateral, the degree with the largest angle is;
Third, solve the problem (this big question is ***3 small questions, 6 points for each small question, *** 18 points)
17, as shown in the figure, point E is the point on AB, point F is the point on DC, and point G is the point on BC extension line.
(1) If ∠B=∠DCG, which two straight lines are parallel can be judged? Please explain the reasons;
(2) If ∠DCG=∠D, which two straight lines are parallel can be judged? Please explain the reasons;
(3) If ∠ dfe+∠ d = 180, which two straight lines are parallel can be judged? Please provide a justification for the answer.
18, as shown in the figure, the coordinates of point A and point B in △AOB are (2,5) and (6,2) respectively. Translate △AOB down by 3 units and left by 2 units to get △CDE.
(1) Write the left side of C, D and E, and draw the △CDE in the picture.
(2) Find the area of △CDE.
19, an isosceles triangle is formed by a string with a length of 20cm.
(1) If the waist is twice as long as the bottom, what is the length of each side?
(2) Can an isosceles triangle with a side of 5cm be formed? Give reasons
Iv. Answering questions (this big question is ***2 small questions, each small question is 10, and ***20 points)
20. As shown in figure 1, it is known that straight lines l 1∑l2, l3 and l 1, L2 intersect at point A and point B respectively, and point P is on line AB.
(1) Try to find out the equation relationship between ∠ 1, ∠2 and ∠3, and explain the reasons;
(2) Apply the conclusion of (1) to solve the following problems.
○ 1 As shown in Figure 2, point A is 40 northeast of point B,
Point A is 45 northwest of point C. How about ∠BAC?
○2 In Figure 3, the blade of the knife is ∑ up and down, and the shape of the handle is a right-angled trapezoid (a small semicircle is cut from the bottom). What is the degree of ∠ 1+∠2?
2 1, as shown in the figure, on a square grid with the vertex of square ABFG and square CDEF and the side length of 1.
(1) Establish a plane rectangular coordinate system, so that the coordinates of point B and point C are respectively
Are (0,0) and (5,0),
Write the coordinates of points a, d, e, f and g?
(2) Connect BE and CG to intersect at H point, and measure the length of BE and CG and the degree of ∠BHC with geometric tools.
V. The topic of study (the big topic * * 1 small topic, *** 14 points)
22. We know that among triangles, a triangle with an obtuse angle is called an obtuse triangle; A right triangle is called a right angle; A triangle with three acute angles is called an acute triangle.
As shown in the figure, a piece of paper with an acute triangle ABC is cut into n (n≥2) small triangles with scissors (these small triangles can still be put back into the original triangle).
(1) When n=2, how many possibilities are there for these two triangles to be classified by angle? Draw all the possibilities in the spare diagram one by one and fill in the corresponding numbers: (the spare diagram may not be used up)
(2) When n=3, three triangles can be divided into eight possibilities according to the angle, and all the possibilities can be drawn in the diagram one by one according to the specified position.
(3) When n=4, all four triangles can be obtuse triangles, right triangles and acute triangles. Draw them one by one in the picture.
Reference answer:
1. Multiple-choice questions (this big question is ***8 small questions, with 3 points for each small question and 24 points for * * *). Only one of the four options given in each small question is correct. Please put the letters before the correct answer in brackets after the question.
1.B 2。 C 3。 D 4。 B 5。 B 6。 D 7。 C 8。 B
Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question and 24 points for * * *).
9. ∠ 2 =142, ∠ 3 = 38, ∠ 4 =14210. The vertical segment is the shortest.
1 1.6 or 2cm12.168cm213. (-3,-4), (-4,-3), (-6,-2)
14. Line15. 6, 7, = 16. 125.
Third, solve the problem (this big question is ***3 small questions, 6 points for each small question, *** 18 points)
17. Solution: (1)∵∠B=∠DCG, ∴∥ab∨CD (same angle, two straight lines are parallel). ..............................................................................
(2)∫∠DCG =∠d, ∴AD∥BC (internal angles are equal and two straight lines are parallel) ...........................................................................................................
(3) ∵ ∠ DFE+∠ D = 180, ∴AD∥EF (with complementary inside angles and parallel lines) ... 6 points.
18. solution: (1) c (0,3), d (-2,3), e (4,4-1), .............................................................................................
Four points are omitted from the figure.
(2) 6 points.
19. Solution: (1) Let the base length be x, then the waist length is 2x.
Solution:
The length of each side is 4cm, 8cm and 8cm, respectively. 3 points for .................................................................................................................................
(2) When the bottom length is 5cm, the waist length is (cm).
When the waist length is 5cm, the bottom length is (cm).
∫5+5 = 10, ∴ You can't form an isosceles triangle with a waist length of 5 cm. ............................................................. scored 5 points.
An isosceles triangle with a base length of 5cm can be formed. At this time, the three sides are 5 cm, 7.5 cm, 7.5 cm ... 6 points respectively.
Iv. Answering questions (this big question is ***2 small questions, each small question is 10, and ***20 points)
20. Proof: (1) ∠ 1 ∠ 2 = ∠ 3. ......................................................................................................................
∵ ∥
∴∠ 1+∠pcd+∠pdc+∠2= 180
In △PCD, ∠ 3+∠ PCD+∠ PDC = 180.
∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠873
(2) ① ∠ BAC = ∠ DBA+∠ ACE = 40+45 = 85 ......................................... 6 points.
②∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠87
2 1. Solution: (1) Establish a plane rectangular coordinate system according to known conditions (as shown in the figure).
A (-3，4)，D(8 ^ 8， 1)，E(7 ^ 7，4)，F(4 ^ 4，3)，G ( 1，7)。
(2) the connecting line BE and CG intersect at point h,
The measured length of BE and CG: be = CG ≈ 8. 1 ..............................................................................................................................................
Measurement ∠ BHC: ∠ BHC = 90 ............................................... 8 points.
V. The topic of learning (this big topic * *1,*** 1 4 points)
22. Solution: (1) When classified by angle, there are two possibilities: ........................................ 1 min.
1 obtuse triangle 0 obtuse triangle
0 right triangles, 2 right triangles
1 acute triangle 0 acute triangle 3 points.
(2) At an appropriate time, all possible positions are drawn on the map:
3 obtuse triangles 2 obtuse triangles 2 obtuse triangles 1 obtuse triangles
1 right triangle 1 acute triangle 2 right triangle
3 right triangles 2 right triangles 1 obtuse triangles 1 obtuse triangles
1 acute triangle 2 acute triangle 1 right triangle
1 acute triangle
........................... 1 1 min.
(3) When, four are obtuse triangles, right triangles and acute triangles, which are drawn one by one in the figure respectively:
4 obtuse triangles 4 right triangles 4 acute triangles 14 points