Math 6 Chapter 1 Lesson 3: Line passing through two points
1. Summary of theory Tóm
1.1. Draw a line
To draw a line passing through two points A and B we do the following:
– Place the edge of the ruler passing through two points A and B
– Use a pencil to trace along the edge of the ruler
Comment: There is a straight line and only one line passing through two points A and B.
1.2. Line name
We already know how to name a line with a lowercase letter.
Because the line is defined by two points, we also use the names of those two points to name the line, for example, we call the line passing through two points A and B the line AB or the line BA.
We also name the line with two lowercase letters, for example, the line xy and yx.
1.3. Lines that coincide, intersect, are parallel
In Figure 19, the two lines AB and AC have only one point in common, A. We say they intersect and A is the intersection of those two lines.
The two lines xy and zt in figure 20 have no common ground (even if they extend forever in both directions), we say they are parallel.
Attention:
Two lines that do not coincide are also known as two distinct lines.
Two distinct lines either have only one point in common or have no points in common,
2. Illustrated exercise
Question 1: Given three points A, B, C that are not collinear. Draw lines passing through pairs of points.
a. How many straight lines in all?
b. Write the names of the lines.
c. Write the name of the intersection of each pair of lines.
Solution guide:
a. 3 straight lines
b.
Line AB
Line BC
straight line CA
c.
The intersection of line AB and line AC is A .
The intersection of line AB and line BC is B
The intersection of line BC and line CA is C
Verse 2: Given three points R, S, T collinear:
a. Name the line in any way possible.
b. Why say those lines overlap.
Solution guide:
a. There are 6 ways to write the line name in the picture: RS line, RT line, etc.
b. The above 6 lines overlap because they are just one line
Question 3: Draw a line a. Take \(A \in a,\,B\, \in b,\,C \in c,\,D \notin a.\) Draw lines passing through pairs of points.
a. How many lines can be drawn in all (distinct)
b. Write the names of those lines.
c. D is the intersection of the lines.
Solution guide:
a. There are 4 distinct lines
b. Those are straight lines: DA, DB, DC, a
c. D is the intersection of 3 lines DA, DB, DC
We say: The three lines DA, DB, DC are concurrent at D.
3. Practice
3.1. Essay exercises
Question 1: Given three straight lines. Draw the figure in the following cases:
a. They have 1 intersection.
b. They have 3 intersections.
c. They have no intersection.
Verse 2: Draw 4 lines that intersect each other in pairs in the following cases:
a. They all have 1 intersection
b. They have all 4 intersections
c. They have all 6 intersections
Question 3: Draw a 5pointed star as shown
a. Name the intersection points on the figure.
b. Read the names of sets of 4 collinear points.
c. Five intersecting lines from pair to one give at most the loss of intersection.
d. Draw another shape with 5 intersecting lines one by one and give 10 intersections.
3.2. Multiple choice exercises Bài
Question 1: Given two ladders a, b. Then a, b can
A. Parallel
B. Duplicate
C. Cut each other
D. All three answers above are correct
Verse 2: Select the correct answers:
A. Through two distinct points there are infinitely many lines
B. There are infinitely many points on the same line
C. Two distinct lines are parallel
D. Of the three collinear points, two lie between
Question 3: Given three points A, B, C that are not collinear. Draw a line passing through pairs of points. What lines can be drawn?
A. AB, BC, CA
B. AB, BC, CA, BA, CB, AC
C. AA, BC, CA, AB
D. AB, BC, CA, AA, BB, CC
Question 4: Given 5 points A, B, C, D, E of which no three points are collinear. Draw a line passing through pairs of points. How many lines can be drawn?
A. 25
B. 10
C. 20
D. 16
Question 5: Given 3 distinct lines a, b, c. In which case the three lines are redundant and have no intersection?
A. three double straight lines intersect each other
B. a intersects b and a parallel to c
C. three double lines one parallel
D. a is parallel to b and a intersects c
Question 6: Given 100 points where none of the 3 points are collinear. How many lines can be drawn through pairs of points.
A. 4950 straight lines
B. 4590 straight lines
C. 9900 straight lines
D. 100 straight lines
Verse 7: Given a number of points where no three points are collinear. Draw a line passing through pairs of points. The total number of lines drawn is 21. How many points are there given?
A. 6
B. 10
C. 12
D. 7
Verse 8: For drawing:
How many distinct lines are there in the figure?
A. 5
B. 6
C. 7
D. 8
Verse 9: For drawings
How many points are the intersection points of exactly two lines?
A. 5
B. 6
C. 10
D. 12
Question 10: Given 50 points, none of which are collinear. Draw lines passing through pairs of points. How many lines can be drawn in all?
A. 1225
B. 1275
C. 2450
D. 2550
Question 11: Choose the correct statement?
A. There are infinitely many lines passing through 2 points
B. There is at least 1 straight line passing through 2 given points
C. There is 1 and only 1 line passing through two given points
D. There are 2 lines passing through 2 points
Verse 12: Given 3 distinct lines a, b, c. How many intersections can there be at most?
A. 1 intersection
B. 2 intersections
C. 3 intersections
D. countless intersections
4. Conclusion
Through the lecture, The line passes through these two points, you need to complete some of the objectives given by the lesson, such as:

Know how to draw lines and how to name lines.

Lines coincide, intersect, and are parallel.
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