Junior high school mathematics volume 2 Chapter 5 Axisymmetric life training questions:
First, multiple-choice questions (3 points for each question, ***30 points)
1. The following patterns are the symbols of several domestic banks, among which the non-axisymmetric one is ().
2. The following are four Chinese characters, among which the one with axisymmetric graphics is ().
A.B. C. D。
As shown in the figure, a triangle has three residential quarters (A, B, C). Now it is decided to build a shopping supermarket between three quarters, so that the distance from the supermarket to the three quarters is equal, so the supermarket should be built in ().
A. intersection of high lines on both sides of AC and BC B. intersection of at and midline on both sides of BC.
C. at the intersection of the median vertical lines on both sides of AC and BC. Where is it? Answer: At the intersection of the two bisectors of the inner corner.
4. As shown in the figure, straight lines L 1, L2 and L3 represent three intersecting expressways.
Now it is necessary to build a cargo transfer station, which is required to be equidistant from three highways.
Then the available addresses are () A. One B. Two C. Three D. Four places.
5. The symmetry axis of isosceles triangle is ()
A. the bisector of the vertex B. the height of the bottom C. the center line D. the straight line where the height of the bottom is located
6. As shown in the figure, if the degree is ()
A.B. C. D。
7. The following statement is incorrect ()
A. If two figures are symmetrical about a straight line, then the symmetry axis is the middle vertical line connecting the corresponding points.
B. If two figures are symmetrical about a straight line, they can overlap.
C. an isosceles triangle is an axisymmetric figure.
D. there is only one symmetry axis of the line segment.
8 .. As shown in the figure, in the quadrilateral ABCD, the AB side and the AD side are symmetrical about AC, so the following conclusion is correct ().
1 ca split equally? BCD2 AC split? Not good; ③DB？ AC； ④BE=DE。
A.② B.①② C.②③④ D.①②③④
9. Which mirror is his image ()
10. An isosceles triangle, not an equilateral triangle, has * * * () bisectors, heights and midlines.
a9b . 7c . 6d . 3
Fill in the blanks (3 points for each question, 30 points for * * *)
1 1. Observe the following English letters, among which there are _ _ _ axisymmetric figures.
A, China, Germany, Britain, France, Spain, Japan, South, China, Britain, Z.
12. One internal angle of an isosceles triangle is 700, so the degrees of the other two angles are _ _ _ _ _.
13. As shown in the figure, in the triangle ABC, AB=AC,? A=40 degrees,
The perpendicular line MN of AB crosses AC to D, and then connects BD. DBC is equal to _ _ _ _ degrees.
14. The two triangles shown in the figure are symmetrical about a straight line. 1= 1 10? ,? 2=46? ,
Then x=
15. As shown in the figure, the actual number in the mirror is _ _ _ _ _ _ _ _.
16. As shown in the figure, in △ABC,? C=90？ , AD divides BAC equally.
If BC intersects D and the distance from D to AB is 5cm, then CD = _ _ _ _ cm.
17. it is known that AD is the height of equilateral △ABC, and BE is the center line of AC side.
AD and BE intersect at point f, then? AFE=______。
18. The figure is an axisymmetric figure, and the straight line where AD is located is the axis of symmetry.
Look at the chart carefully and answer the following questions:
(1) The symmetrical line segment between BO and CF is _ _ _ _ _ _ _ _;
(2) the symmetrical triangle of delta ace is _ _ _ _ _ _ _.
19. The reflection of the license plate in the water is shown in the figure.
Then the license plate number of this car is _ _ _ _ _ _ _.
20. Xiaoming folded a rectangular piece of paper twice and drew a quadrilateral.
Then cut out the pattern (hollowing out) and unfold the rectangular paper to obtain the following pattern.
Set the crease to, observe the figure and fill in the blanks:
Quadrilateral ① and Quadrilateral ② are symmetrical about _ _ _ _ _ _;
The crease is not only the symmetry axis of _ _ _ _ and _ _ _ _;
It is also the axis of symmetry between _ _ _ _ and _ _ _ _ _;
On the whole, it is also the axis of symmetry between _ _ _ _ and _ _ _ _.
Iii. Answering questions (***40 points)
2 1. (The full mark of this question is 10) As shown in the figure, take AB as the axis of symmetry, and draw a symmetrical figure of each figure.
22. (full mark of this question 10) As shown in the figure, the known points m, n and? AOB, find a point p, so that the distance from p to point m and n is equal, and to? The distance on both sides of AOB is equal.
23. (The full mark of this question is 10) As shown in the figure, in △ABC, what are AB=AC and AD? The bisector of BAC,
And then what? 2=25? , beg? BAC and? The degree of B.
24. (The full score of this question is 10) as shown in the figure, △ABC,? BAC= 1 100, DE and FG are the vertical lines of AB and AC respectively, and E and G are vertical feet respectively.
(1) Q? The degree of DAF.
(2) If BC < 10 cm, find the perimeter of △DAF.
Axisymmetric test in life (2)
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1. The circle is an axisymmetric figure, and its axis of symmetry is ().
A. 1 Article B.2
C.3d. Many articles
2. As shown in figure 1,? 1=? 2、PD？ AB，PE？ BC, the vertical feet are D and E respectively, so the wrong conclusion is ().
A.PD=PE B.BD=BE C？ BPD=？ BPE BP
3. As shown in Figure 2, it is the symbol of several domestic banks, in which the axisymmetric figure is ().
Figure 2
1。
4. As shown in Figure 3, is it known? AOB and a fixed-length line segment a, in? Find a point in AOB, the distance from P to angles OA and OB 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) work? The bisector OP of AOB intersects 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, the internal angle is 60? Then this triangle is ().
A. equilateral triangle B. isosceles right triangle
C. isosceles triangle D. including 30? Right triangle of angle
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, B.3, C.2 and 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 overlapping part of an isosceles triangle _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
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 vertex angle of an isosceles triangle is 70? , base 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 soon 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. So 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)
The first grade mathematics book 2 Chapter 5 Answers to the axisymmetrical training questions in life:
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 do point b, about the symmetrical point b of straight line l? ,
Link AB? Cross l at point p, then point p is the drinking point. In terms of symmetry, PB=PB? .
∫ Take a little p from L? , link AP? 、P？ B, from the sum of two sides of a triangle is greater than the third side, we know.
AP？ +P？ b？ & gtAB？ =PA+PB？ ,
Is that AP? +P？ b？ & gtPA+PB。
? Only at point P can PA+PB be minimized.
24. Work? People's bisector OC,
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, where is the criminal? On the bisector of MON, the point p is also above).
The distance between the points on the perpendicular bisector of the line segment and the points at both ends of the line segment is equal (so the point P is on the perpendicular bisector of the line segment AB).
? The intersection of two straight lines, that is, point P, meets the requirements.
25. The height of the mirror is at least half the height.
26. reasonable.