## Math 6 Chapter 1 Lesson 2: Three points in line

## 1. Summary of theory Tóm

### 1.1. What are three collinear points?

When three points A, C, and D are on the same line, we say they are collinear.

When three points A, B, and C are not on the same line, we say they are not collinear.

### 1.2. Relationship between three collinear points

With three collinear points A, C, B as shown in the figure, we can say:

– Two points C and B are on the same side of point A

– Two points A and C lie on the same side of point B

– Two points A and B are on the opposite side of point C

Point C lies between two points A and B.

**Comment:** Of the three collinear points, there is one and only one that lies between the other two.

## 2. Illustrated exercise

**Question 1: **Look at the picture and read the name of the point between the other two points.

**Solution guide:**

Point I lies between two points A and M

Point I lies between two points B and N

Point N lies between two points A and C

Point M lies between two points B, C

**Verse 2: **Draw three points M, N, P in a straight line such that:

a) N, P are on the same side with respect to M

b) M, P are on the opposite side of N

c) M lies between N and P

**Solution guide:**

a. N, P are on the same side with respect to M: Cases 1, 3, 4, 5

b. M, P are on the opposite side of N: Cases 1, 5

c. M lies between N and P: Cases 2, 6

**Question 3: **Draw three points A, B, C in a straight line so that point B lies between two points A and C. How many cases are there in the figure?

**Solution guide:**

There are two cases of the figure. In each case, point B lies between A and C.

## 3. Practice

### 3.1. Essay exercises

**Question 1:**

a. Given three points A, B, and C on a straight line, how many cases are there in the figure?

b. In each case, how many points are in between the other two?

c. Let’s say how to draw three points that are not collinear.

**Verse 2: **

Read the names of the collinear triples in the figure.

**Question 3: **Draw each figure according to the wording in each of the following cases.

a) Three points A, B, C are collinear and point C lies between two points A and B.

b) Three points M, N, P are collinear and two points M, N are on the same side with respect to point P.

c) Three points X, Y, Z are collinear and two points X, Y are on the opposite side of point Z.

d) Four points E, F, G, H lie on the same line and point G lies between two points E, F and two points E and H lie on the opposite side of point F.

e) Four points R, S, T, S lie on the same line, and two points T and S lie on the same side of point U and two points R and T lie on the opposite side of point U.

### 3.2. Multiple choice exercises Bài

**Question 1: **Select the correct answers

A. If three points are on the same line, those three points are not collinear

B. If three points are not on the same line, then the three points are collinear

C. If three points are on the same line, then the three points are collinear

D. All three answers above are wrong

**Verse 2: **Given three points M, N, P collinear with P between M and N. Choose the correct figure

**3: **Name the trio of collinear points in the figure below

A. A, O, D and B, O, C

B. A, O, B and C, O, D

C. A, O, C and B, O, D

D. A, O, C and B, O, A

**Question 4: **How many sets of three points are collinear in the following figure?

A. 10

B. 11

C. 12

D. 13

**Question 5: **For the following figure. Choose the wrong statement

A. Three points D, E, B are collinear

B. Three points C, E, A are not collinear

C. Three points A, B, F are collinear

D. Three points D, E, F collinear

**Question 6: **How many sets of collinear points are there in the figure below?

A. 7

B. 4

C. 5

D. 6

## 4. Conclusion

Through this three-point line lesson, you need to complete some of the objectives given by the lesson, such as:

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