The first volume of seventh grade math comparison line segment length test: 1. Multiple choice questions (4 points for each small question, *** 12 points)
1. The following four life and production phenomena:
(1) physical education class, the teacher checks whether the team is in a straight line and only looks at the first student; (2) When planting trees, as long as the positions of two trees are determined, the straight line of the same row of trees can be determined; (3) When installing wires from A to B, always try to install them along the AB line; (4) Straightening curved roads can shorten the distance,
Which one is available? Between two points, the line segment is the shortest? Explain this phenomenon is ()
A.①② B.①③ C.②④ D.③④
2. For example, a fountain pen is placed right next to a ruler, and Xiao Ming finds that the pen tip (point A) of the fountain pen is just about 5.6cm opposite to the scale, and the other end (point B) is just about 20.6cm opposite to the scale, so the scale at the midpoint of the fountain pen is about ().
A.15cm B.7.5cm c. 13. 1 cm d. 12. 1 cm.
3. As shown in the figure, fold a rope into a line segment AB, and cut the rope from point P, and it is known that AP= PB. If the longest length of the cut rope is 40cm, then the original length of the rope is ().
A.30cm B.60cm C.120cm D.60cm or120cm
Fill in the blanks (4 points for each small question, *** 12 points)
4. The line segment AB=4. If BC= 1 is intercepted on the line segment AB, then AC=.
5. For example, extending the line segment AB to C makes BC=4. If AB=8, the length of the line segment AC is twice that of BC.
6. For example, it is known that B is the midpoint of AC and C is the midpoint of BD. If BC=2cm, then AD= cm.
Iii. Answering questions (***26 points)
7.(8 points) As shown in the picture, A and B are two villages. If you want to build a pump station on the L River to deliver water to two villages, ask where the pump station should be built by the river to make the pipeline shortest, and explain the reasons.
8.(8 points) For example, it is known that C is the midpoint of AB, D is the midpoint of AC, and E is the midpoint of BC.
(1) If DE=9cm, find the length of AB.
(2) If CE=5cm, find the length of DB.
Extension extension
9.( 10) (1) It is known, for example, point C is on the AB line, line segment AC= 15, BC=5, and point M and point N are the midpoint of AC and BC respectively, so find the length of MN.
(2) According to the calculation process and results of (1), let A C+BC=a, and other conditions remain unchanged. Can you guess the length of MN? Please use concise language to express the law you found.
(3) What if (1)? Point c is on the AB line? Change to? Point c is on the straight line AB? Other things being equal, what is the result? Please explain your reasons.
Analysis of the answer to the length test of mathematical comparison line segment in the first volume of the seventh grade: 1. D.①② Phenomenon analysis can be explained by two points that can determine a straight line; ③ ④ This phenomenon can be explained by the shortest line segment between two points.
2. Decomposition C. Because the pen tip (point A) of fountain pen is just opposite to the ruler with a scale of about 5.6cm, and the other end (point B) is just opposite to the ruler with a scale of about 20.6cm, the length of fountain pen is 20.6-5.6= 15(cm), and one and a half of fountain pen is = 15. 2=7.5 (cm), so the scale of the pen midpoint is about 5.6+7.5= 13. 1 (cm).
3. analytical choice D. there are two situations in this question:
When point A is the folding point of the rope, unfold the rope as shown.
Because AP∶BP= 1∶2, the longest section of the cut rope is 40cm, so 2AP=40cm, so AP=20cm, so PB=40cm.
So the original length of the rope =2AB=2(AP+PB)=2? (20+40)= 120 (cm).
When point B is the folding point of the rope, unfold the rope as shown.
Because AP∶BP= 1∶2, the longest rope is 40cm, so 2BP=40cm, so BP=20cm, so AP= 10cm.
So the original length of the rope =2AB=2(AP+BP)=2? (20+ 10)=60 (cm).
To sum up, the original length of the rope is 120cm or 60cm.
4. Analytic AC=AB-BC=4- 1=3.
Answer: 3
What are the conditions in the alternative topics? On line AB? What if it is changed? On the straight line AB? , other conditions unchanged, then AC=.
There are two kinds of analysis.
When c is between a and b, AC=3.
When c is on the extension line of AB,
AC=AB+BC=4+ 1=5。
Answer: 5 or 3
5. Analysis Because BC = 4, AB = 8 and AC= 12, the length of line segment AC is three times that of BC.
Answer: 3
6. Analysis shows that B is the midpoint of AC, and if BC=2cm,
AC = 4 cm, BD = 4 cm,
Then AD=AC+BD-BC=6(cm).
Answer: 6
7. For example, intersection points A and B are line segments AB, and intersection point P with straight line L is the point of pumping station, because the line segment between two points is the shortest.
8. Analysis (1) Because D is the midpoint of AC and E is the midpoint of BC,
So AC=2CD, BC= 2CE,
So AB=AC+BC=2DE= 18cm.
(2) Because E is the midpoint of BC, BC=2CE= 10cm.
Because c is the midpoint of AB and d is the midpoint of AC,
So DC= AC= BC=5cm,
So DB = DC+CB = 5+ 10 = 15 (cm).
9. Analysis (1) Because points M and N are the midpoint of AC and BC respectively,
So MC= AC=? 15=，NC= BC=，
So MN=MC+NC= 10.
(2) The length of 2)MN is.
It is known that the line segment is divided into two parts, and the distance between their midpoints is equal to half the length of the original line segment.
(3) Case discussion: When point C is on the AB line, Mn = AB = 1 0 is obtained from (1);
When point c is on the extension line of line AB, as shown in.