2. As shown in the figure, lines A and B are cut by a third line C. If A∨B, ∠ 1 = 50, then ∠ 2 =.
3. In the plane rectangular coordinate system, the point (x2+ 1, -3) is in the fourth quadrant.
4. As shown in the figure, in △ABC, BD is the bisector, BE is the midline, if AC=24cm, AE= cm, if ∠ ABC = 72, then ∠ABD= degrees.
5. If point A (-2, n) is on the X axis, the coordinates of point B (n- 1, n+ 1) are.
6. Place a pair of right-angle triangular plates as shown in the figure, so that the right-angle edge of the triangular plate with an angle of 30 coincides with one right-angle edge of the triangular plate with an angle of 45, then the degree of ∠ 1 is degrees.
7. Given (a-2)2+|b+3|=0, the coordinate of P(-a, -b) is .8. The sides of an isosceles triangle are 3 and 7 respectively, and the circumference is 0.
9. Make a regular pentagonal paper (Figure ①) into an open carton with a regular pentagonal bottom and the same height (the sides are perpendicular to the bottom, as shown in Figure ②). If you need to cut off a quadrilateral at each vertex, such as quadrilateral ABCD in Figure 1, then the size of ∠BAD is the degree.
10. The picture shows the newly-built rectangular ABCD flower field in Huanggang Middle School, with a length of AB= 100m and a width of AD = 50 m. Now a winding scenic path has been built in the field. The width of the middle road from entrance A and entrance B is 1m, the width of the road at the intersection of the two paths is 2m, and the rest are planted with lawns, so the path area is m2.
2. Fill in the blanks (this big question is ***6 small questions, 3 points for each small question, * * 18 points) 1 1. In the figure below, ∠ 1 and ∠2 are opposite, which is () A.B.C.D
12. Point P is in the second quadrant, the distance from P to X axis is 4, and the distance from Y axis is 3, so the coordinate of point P is () A. (-4,3) B. (-3,4) C. (-3,4 4) D. (3 3,4).
13. As shown in the figure, it is () A. (2) (3) B. (2) (3) (4) C. (1) (2) (4) D.
14. With the following groups of line segments as sides, a triangle can be formed by () A.2cm, 2cm, 4cmB.2cm, 6cm, 3cmC.8cm, 6cm, 3cmd. 1 1cm, 4cm and 6cm.
15. As shown in the figure, the coordinates of A and B are (2,0) and (0, 1) respectively. If the translation of line segment AB is A 1B 1, the value of a+b is () A.2B.3C.4D.5
16. If the two sides of ∠ α and ∠βare parallel, and the cubic difference between ∠αand ∠βis 36, then the degree of ∠αis () A. 18 B. 126 C.
Third, solve the problem (***8 questions, * * 72 points) 17. As shown in the picture, Xiao Cong plays an origami game with a rectangular paper ABCD that is broken on both sides. After he folded the paper along EF, point D and point C fell at the positions of D' and C' respectively, and measured ∠ EFB with a protractor.
18. Complete the following proofs: Known, as shown in the figure, AB∨CD∨GH, EG ∠BEF, FG ∠EFD.
Verification: EGF = 90.
Proof: ∫HG∨AB (known)
∴∠ 1=∠3
Also: mercury ∨ cadmium (known)
∴∠2=∠4
∫AB∑CD (known)
∴∠BEF+ = 180
Also ∵EG bisects ∠BEF (known)
∴∠ 1= 12∠
And ∵FG bisection ∠EFD (known)
∴∠2= 12∠
∴∠ 1+∠2= 12( )
∴∠ 1+∠2=90
∴∠ 3+∠ 4 = 90, that is ∠ EGF = 90.
19. In the rectangular coordinate system shown in the figure, the coordinates of point A and point B are (-3,0) and (-2,4) respectively.
(1) please track these two points in this coordinate system;
② Find the area of △AOB.
20. As shown in the picture, there are two sand carriers A and B sailing on the Yangtze River in the golden waterway. Ship A measured that the beacon light C was in the direction of 52 east-north and ship B was in the direction of 82 east-north. At this time, Ship B measured that the beacon light C was in the direction of 36 north by west. Now, can you help ship B calculate its angle of view ∠ABC?
2 1. As shown in the figure, CD⊥AB is in D, EF⊥AB is in F, ∠ 1=∠2. DG∨ Is it BC? If they are parallel, please explain why.
22. If the coordinates of two vertices of a square are (2,2) and (4,2), please establish an appropriate rectangular coordinate system to draw the position of the square and write all possible coordinates of the other two points. Show analysis 23. As shown in the figure, △ABC, AE and BF are bisectors of angles, and they intersect at point O (∠ABC >∞).
(1) Try to explain ∠ boa = 90+12 ∠ c;
(2) When 2)AD is high, judge the relationship between ∠DAE and ∠C and ∠ABC, and explain the reasons.
24. As shown in the figure: AB∑CD, the straight line L intersects AB and CD at points E and F respectively, the point M is on EF, and n is the moving point on the straight line CD (points N and F do not coincide).
(1) When point N moves on ray FC, ∠FMN+∠FNM=∠AEF, explaining the reason;
(2) When point N moves on ray FD, what is the relationship between ∠FMN+∠FNM and ∠AEF and explain the reasons.