Test site mapping? Similar transformation.
Analysis point a is AD? BC is equal to d, which can be found by the complementary angle of equal angle? Bad =? C, it can be judged that △ABD is similar to △CAD.
Solution: As shown in the figure, AD has.
18. In order to further change the mathematics teaching of grade seven in a school and improve students' interest in learning mathematics, the Academic Affairs Office of the school randomly selected six students from each class of grade seven and conducted a questionnaire survey on their mathematics learning. Judging from the topic of the survey, we divide the students' answers to the degree of their liking for mathematics learning into:? Like it very much? 、? B: better? 、? Isn't it true? 、? Don't you like it very much? In order to solve this problem, the questionnaire requires each student to choose one and only one. The results are counted out. Now draw the statistical results into the following two incomplete statistical charts.
Please answer the following questions based on the information provided above:
(1) Complete the bar chart and fan chart above;
(2) The mode that students like mathematics learning is preferred;
(3) If there are 960 students in the seventh grade of our school, would you please estimate the mathematics learning situation among the students in this grade? It's not true? How many people are there?
Number of test sites; Estimate the population with samples; Department statistical chart; Bar chart.
According to the histogram and fan chart, the number of students surveyed is analyzed (1), so as to determine the number of students who choose B and the percentage of students who choose B and D, thus completely supplementing the statistical chart;
(2) According to the completed bar chart in (1), the pattern can be obtained;
(3) According to the fan-shaped statistical chart completed in (1), students' understanding of mathematics learning in this grade can be obtained. It's not true? Number of people.
Solution: (1) can be obtained from the meaning of the question.
The students surveyed are: 30? 25%= 120 (person),
The students who choose B are: 120- 18-30-6 = 66 (person),
The percentage of b is: 66? 120? 100%=55%,
The percentage of d is: 6? 120? 100%=5%,
Therefore, the completed bar and fan charts are displayed on the right.
(2) According to the bar chart completed in (1),
The mode that students like math learning is: like,
So the answer is: I prefer it;
(3) From the department statistics table completed in (1),
How are the students in this grade studying math? It's not true? Yes: 960? 25%=240 (people),
That is, the students in this grade are learning mathematics? It's not true? There are 240 people.
19. As shown in the figure, in? In ABCD, connect BD, take a little E on the extension line of BD and a little F on the extension line of DB, so BF=DE, connecting AF and CE.
Proof: AF∨CE.
The nature of the parallelogram in the examination center; Congruent triangles's judgment and nature.
Analyze the properties of parallelogram, and get AD∨BC, AD=BC. Proof? 1=? 2, DF=BE, prove that the corresponding angles of △ ADF △ CBE are equal by SAS, and then draw a conclusion from the judgment of parallel lines.
The solution proves that the quadrilateral ABCD is a parallelogram,
? AD∨BC，AD=BC，
1=? 2,
BF = DE，
? BF+BD=DE+BD，
That is, DF=BE,
In △△ADF and △△CBE,
,
? △ADF?△CBE(SAS)，
AFD=？ CEB，
? AF∨CE。
20. In order to build a forest city, set up a new landmark of the city, and realize the development concept of green * * *, a city built in the south of the city? Wang Yue Pavilion? There is also a singing park. Do Xiao Liang, Xiao Fang and other students want to use some measuring tools and geometric knowledge to measure? Wang Yue Pavilion? Height, to test their ability to master knowledge and use knowledge. After observation, they found that the observation point and? Wang Yue Pavilion? The distance between the bottom and the bottom is not easy to measure, and it needs to be measured twice after the study, so they measure it with a flat mirror first. The method is as follows: As shown in the picture, Xiao Fang is in Liang Xiaohe? Wang Yue Pavilion? Place a plane mirror on the straight line BM between them and make a mark on the mirror. The corresponding position of this mark on the straight line BM is point C, and the mirror does not move. Xiao Liang looked at the mark on the mirror. He walked back and forth. What did he see when he reached the D point? Wang Yue Pavilion? The image of vertex A on the mirror surface coincides with the mark on the mirror surface. At this time, the height of Liang Xiao's eyes from the ground was measured as ED = 1.5m, and CD = 2m. Then, in the sun, they made a second measurement by measuring the shadow length. The method is as follows: As shown in the figure, Liang Xiao walks from point D along DM direction 16m, and arrives? Wang Yue Pavilion? At the end f of the shadow, at this time, the shadow length FH = 2.5m, FG =1.65m..
As shown in the figure, AB? BM，ED？ BM，GF？ BM, which ignores the thickness of the plane mirror used in the measurement. Please look it up according to the relevant information provided in the question. Wang Yue Pavilion? The height of AB is the length.
Similar triangles's application.
△ABC∽△EDC, △ABF∽△GFH are obtained according to the principle of specular reflection and similar triangles's judgment method, and then the length of AB is obtained by using the properties of similar triangles.
Solution: from the meaning of the question:? ABC=？ EDC=？ GFH=90？ ,
? ACB=？ ECD，？ AFB=？ GHF，
Therefore, △ABC∽△EDC, △ABF∽△GFH,
=, =,
That is =, =,
Solution: AB=99,
A:? Wang Yue Pavilion? The height of AB is 99m.
2 1. At 7 o'clock yesterday morning, Xiaoming left home by bus and went to Xi 'an to participate in the middle school students' science and technology innovation competition. After the game, he returned the same day, as shown in the figure, which is a function image between the distance y (km) from Xi 'an and the time x (hours) when Xiaoming left home yesterday.
Answer the following questions according to the picture below:
(1) Find the functional relationship represented by line segment AB;
(2) It is known that Xiao Ming was away from Xi 'an112km at 3pm yesterday. When will he go home?
Application of linear function of test center.
After analysis (1), it can be assumed that the functional relationship represented by line AB is: y=kx+b, which can be solved according to the equations with undetermined coefficients;
(2) Press speed = distance first? Calculate the speed of Xiao Ming's going home according to time, and then press time = distance? Speed, listed formula calculation can be solved.
Solution: (1) Let the functional relationship represented by AB line be: y=kx+b,
According to the meaning of the question,
Solve.
Therefore, the functional relationship represented by line segment AB is: y =-96x+ 192 (0? x？ 2);
(2) 12+3﹣(7+6.6)
= 15﹣ 13.6
= 1.4 (hours),
1 12? 1.4=80 (km/h),
? 80
=80? 80
= 1 (hour),
3+ 1=4 (hours).
He got home at 4 pm.
22. In order to thank the customers of a supermarket, all customers who shop in the supermarket can take part in the lucky draw with the shopping receipt. The prizes are three kinds of bottled drinks, namely green tea, black tea and cola. The lottery rules are as follows: ① As shown in the figure, it is a turntable with uniform material and free rotation. The turntable is divided into five sectors, and each area is written with? Is it okay? 、? Green? 、? Le? 、? Tea? 、? Red? Words; ② Customers who take part in a lucky draw can do it twice? Effective random rotation? When the turntable stops, you can get the text in the area pointed by the pointer. We call this rotation time? Effective random rotation? ); (3) suppose the customer turns the turntable, and after the turntable stops, the pointer points to the boundary between the two areas, and the customer can turn the turntable again until one turn? Effective random rotation? ; (4) When the customer completes a lottery, write two words twice in the area pointed by the pointer. As long as these two words are the same as the two words of the prize name (regardless of the order of the words), you can get a bottle of the corresponding prize; When they are different, you won't get any prizes.
According to the above rules, answer the following questions:
(1) once? Effective random rotation? Available? Le? Probability of words;
(2) A customer takes part in the lucky draw with the shopping receipt of the supermarket. Would you please show the customer twice in the form of list or tree diagram? Effective random rotation? After that, the probability of getting a bottle of coke
Test site list method and tree diagram method; Probability formula.
The analysis (1) is divided into five sectors by the turntable, and each area reads? Is it okay? 、? Green? 、? Le? 、? Tea? 、? Red? Words; The answer can be obtained directly by using the probability formula;
(2) Draw a tree diagram according to the meaning of the question first, and then get all possible results from the tree diagram and go through the customer twice? Effective random rotation? After that, the situation of a bottle of coke is obtained, and the answer can be obtained by solving it with probability formula.
Solution: (1)∵ The turntable is divided into five sectors, and each area is written with? Is it okay? 、? Green? 、? Le? 、? Tea? 、? Red? Words;
? Once? Effective random rotation? Available? Le? The probability of words is:
(2) draw a tree diagram:
∫ * * There are 25 possible outcomes that the customer has passed twice? Effective random rotation? After that, there are two ways to get a bottle of coke.
? The customer passed by twice? Effective random rotation? The probability of getting a bottle of coke after that is:.
23. As shown in the figure, it is known that AB is the chord of ⊙O and point B is BC? AB passes through ⊙O at point C, and the tangent intersection point C is ⊙O at point D. Take the midpoint E of AD, the intersection point E of the extension line is EF∨BC, DC at point F, and connect AF, and the extension line passes through BC at point G. 。
Verification:
( 1)FC = FG；
②AB2 = BC? BG。
Similar triangles's judgment and nature; Vertical diameter theorem; The nature of tangent.
Analysis (1) obtains EF from the properties of parallel lines? AD, FA=FD is obtained from the nature of the median vertical line of the line segment, and what is obtained from the nature of the isosceles triangle? FAD=？ D, prove it? DCB=？ G, which is derived from the equal vertex angle? GCF=？ G, you can draw a conclusion;
(2) Connect AC, prove that AC is diameter ⊙O by the theorem of circle angle, and get it by the theorem of chord tangent angle. DCB=？ Taxi, prove it? CAB=？ G again? CBA=？ GBA=90？ , prove △ABC∽△GBA, and draw the conclusion that the corresponding edges are proportional.
Proof of solution: (1)∵EF∨BC, AB? BG，
? EF? AD，
E is the midpoint of AD,
? FA=FD，
FAD=？ d，
∵GB？ AB，
GAB+？ G=？ D+？ DCB=90？ ,
DCB=？ g，
∵? DCB=？ GCF，
GCF=？ G
,? FC = FG
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