4. As shown in Figure 3, given ∠AOB and a fixed-length line segment A, find a point P in ∠AOB, and the distance between OA and OB on both sides of the angle is equal to A. 。
Practice: (1) as the vertical NH of OB, so that NH = A and H are vertical feet; (2) the crossing point n is nm ∨ ob; (3) The bisector OP of ∠AOB intersects with MN at point P; (4) Point P is what you want. The basis of (3) is ().
A. the distance between parallel lines is equal everywhere.
B the points with equal distance to both sides of the corner are on the bisector of the corner.
The points on the bisector of an angle are equidistant from both sides of the angle.
D the points equidistant from both ends of the line segment are on the middle vertical line of the line segment.
5. As shown in Figure 4, △ABC and △ADE are symmetrical about the straight line L, and the following conclusions are drawn: ① △ ABC △ ade; ②l vertically divide db; ③∠C =∠E； (4) The intersection of 4)BC and the extension line of DE must fall on the straight line L, where () is wrong.
A.0 B. 1
C.2 D.3
6. Among the following four figures, if the figure on the left is folded symmetrically, which one can become the figure on the right ().
Figure 5
7. As shown in Figure 6, two flat mirrors with opposite mirrors are firmly placed on the desktop, and a small stool is placed between the two mirrors, so that the image of the small stool can be obtained in the two mirrors ().
A.2 B.4
C.16 d. countless.
8. If the triangle is an axisymmetric figure with an internal angle of 60, then the triangle is ().
A. equilateral triangle B. isosceles right triangle
C. isosceles triangle D. 30 right triangle
9. The length of the base of an isosceles triangle is 10 cm, and the difference between the perimeters of the triangle divided into two parts by the middle line on a waist is 4 cm, so the waist length of the triangle is ().
Length 6 cm width 14 cm
C.4 cm or 14 cm D.6 cm or 14 cm.
10. As shown in Figure 7, straight lines l 1, l2 and l3 respectively represent three intersecting expressways. Now it is necessary to build a cargo transfer station, and the distance from here to the three highways is equal. I guess the alternate address is ().
A.4 place B.3 place
C.2，D. 1
Fill in the blanks (3 points for each small question, 30 points for * * *)
1 1. If a graph is along a straight line _ _ _ _ _ _ _ _, and the parts on both sides of the straight line can be _ _ _ _ _ _ _ _ _ _, then the graph is called _ _ _ _ _ _ _.
12. "Three lines in one" refers to the coincidence of isosceles triangles _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
13. Xiaoming is standing in front of the mirror. He saw in the mirror that the number on his vest was 80 1, so the actual number on his vest should be _ _ _ _ _.
14. Of the four graphs of straight line, angle, line segment and equilateral triangle, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. The least is _ _ _ _ _ _ _ _, with _ _ _ _ symmetry axes.
15. If the two sides of an isosceles triangle are 4 cm and 9 cm respectively, then its circumference is _ _ _ _ _ _ _ _ cm; If the top angle of an isosceles triangle is 70, the bottom angle = _ _ _ _ _.
16. As shown in Figure 8, DE is the median vertical line of AB and intersects with AC at point D. If AC = 6 cm and BC = 4 cm, the circumference of △BDC is _ _ _ _ _ _.
17. in Chinese characters, there are many axisymmetric figures, such as you, Tian and pin. Please write six more such words: _ _ _ _ _ _ _.
18. Fold a rectangular piece of paper and cut out a pattern. After unfolding, the crease is _ _ _ _ _ of the whole pattern.
19. One day when Xiao Gang looked in the mirror, he saw the clock hanging on the wall behind him, as shown in Figure 9. I guess the actual time should be _ _ _ _ _ _ _.
20. Xiaoming wrote a two-digit number in his exercise book lying flat on the desktop, and Xiaoying stood upright on the desktop with a flat mirror, which is also perpendicular to the two-digit direction. At this time, the two of them saw the actual two-digit number exactly the same as the image in the mirror. Please guess that the two digits written by Xiao Ming in the exercise book may be _ _ _ _ _ _ _ _. (Write at least three. Note: Exercise books and mirrors.
Iii. Answering questions (***60 points)
2 1.(6 points) In an activity, the teacher asked such a question: "How to turn a note into a real equation." The students have been thinking for a long time. At this time, Xiaoying walked to the front of the note and only took out a mirror, which quickly solved the problem. Do you know how Xiaoying did it?
22.(6 points) As shown in figure 10, take the dotted line as the axis of symmetry, please draw the other half of the following pattern.
23.(8 points) Herdsmen graze in A place, and now they have to drive their horses back to their homes in B place, but they have to go to the river to drink water once (as shown in figure 1 1). How should he choose the drinking point P to make the distance Pa+Pb shortest? Why?
24.(8 points) A criminal is escaping along a path with the same distance between two intersecting highways, and two public security personnel who are ambushing in A and B want to catch the criminal at the same time where A and B are at the same distance (as shown in figure 12).
Ask the public security personnel to help with the arrest points in the design drawing and explain the reasons.
25.(8 points) Xiaohong wants to put a toilet mirror in the bedroom so that she can see her whole body. How high (suitable width) should she buy at least?
26.(8 points) When building a house, bricklayers sometimes put an isosceles triangle on the beam (as shown in figure 13) and tie a heavy object from the vertex. If the line that binds the weight just passes through the midpoint of the triangle bottom, the tile union will judge that the beam is horizontal. Is this method reasonable? Please explain your reasons.
27.(8 points) As shown in figure 15, two congruent triangles can be spliced into different figures, and a triangle has been drawn below. Please draw another congruent triangle separately, so that each figure can be made into a different axisymmetric figure. (The drawn triangle can overlap with the original triangle. )
28.(8 points) As shown in figure 16, a floor factory wants to make a batch of square floor tiles. In order to meet the needs of market diversification, it is required that the pattern designed on the floor tile can divide the square into four parts. Please help the factory design the equally divided pattern. (at least six kinds)
answer
I.1.d2.d3.c4.a5.a6.b7.d8.a9.d10.a.
2. 1 1. Fold the axisymmetries that coincide with each other.
12. The bisector of the vertex angle of the center line on the high bottom edge on the bottom edge.
13. 108
14. There are countless angles and line segments on a straight line.
15.22 55
16.10cm
17. Chu, Shan, Ge, Mei, Ye, Jing, Kai ...
18. Axis of symmetry
19.4∶ 15
20.80、30、 10、 1 1、 18、88、…
3.2 1 Using the principle of plane mirror imaging, the plane mirror can be placed on the front, back, left and right sides of the paper strip, as shown in the figure.
22 cents.
23 make point B' the symmetrical point of point b with respect to line l,
Connect AB' and L at point P, then point P is the drinking point. Pb = Pb' from symmetry.
∵ Take any point P' on L to connect AP' and P'B, and the sum of two sides of the triangle is greater than the third side.
AP′+P′B′> AB′= PA+PB′，
That is PA+Pb.
Only at point P can PA+PB be minimized.
24. make the bisector OC of ∠MAN,
Connect AB, and the perpendicular line of the line segment intersects OC at point P, then point P is the capture point.
Reason: the point on the bisector of the angle is equal to the distance between the two sides of the angle (that is, the criminal is on the bisector of ∠MON, and the point P is also on it).
The distance between the points on the vertical line of the line segment and the points at both ends of the line segment is equal (so the point P is vertically bisected by the line segment AB
/article/chuzhong/200703/11928.html (about congruence website)