## Math 6 Chapter 1 Lesson 5: Tia

## 1. Summary of theory Tóm

### 1.1. Ray

The figure consisting of a point O and a part of the line divided by the point O is called a ray of origin O (also known as a half-line of origin O).

### 1.2. Two rays opposite each other

Two rays with common origin Ox and Oy forming a line xy are called opposite rays.

Comment: Each point of a line is the common origin of two opposing rays.

### 1.3. Two rays coincide

Take a point B other than A on ray A.

Ax rays are also known as AB rays. In Figure 29, ray Ax and ray AB are two identical rays.

**Attention:**

Two rays that do not coincide are also known as two distinct rays.

## 2. Illustrated exercise

**Question 1: **On the line x’x there are four points A,B,C,D in that order. In the origin rays B: BA, BC, BD, find:

a) Opposite rays

b) The rays coincide.

**Solution guide:**

a. Opposite rays BA, BC (or BA, BD)

b. The rays coincide: BC, BD.

**Verse 2: **Draw the line xy. Take any point O on xy.

a. Write the names of two rays that share the origin O. Color one of the rays in red. Paint the remaining rays green.

b. Name two opposite rays. What are the characteristics of two opposing rays?

**Solution guide:**

a. Ox rays and Oy rays.

b. Two opposing rays Ox and Oy have two properties: They share the origin O, forming a line xy.

**Question 3: **Draw two opposite rays Ox, Oy.

a. Take \(A \in Ox,\,\,B \in \,\,Oy.\) Write the names of the rays that coincide with the ray Ay.

b. Do two rays AB and Oy coincide? Why?

c. Are two rays Ax and By opposite? Why?

**Solution guide:**

a. Rays that coincide with ray Ay are AO, AB

b. Two rays AB and Oy do not coincide, because they do not have the same origin

c. The two rays Ax and By are not opposite, because they do not have the same origin

**Question 4: **Given three points A, B, C collinear in that order.

a. Of the three points A, B, and C above, which one lies between the other two?

b. Name two opposite rays of origin B.

**Solution guide:**

a. Of the three points A, B, and C that are collinear in that order, then point B lies between the other two points.

b. Ray BA and ray BC are opposite the origin B.

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Given three points A, B, C collinear in that order.

a. Name the rays of origin A, origin B, origin C

b. Write the names of the rays that coincide.

c. Consider the position of point A with respect to ray BA and with respect to ray BC.

**Verse 2: **Draw three points A, B, C so that point B lies between two points A, C. Then name: rays, pairs of opposites, pairs of distinct rays, pairs of coincident rays are in the figure. draw that.

**Question 3: **Draw two rays with common origin Ox and Oy. Take \(A \in Ox,\,\,\,B \in Oy.\) Consider the position of three points A, O, B.

### 3.2. Multiple choice exercises Bài

**Question 1: **Choose the most suitable word or phrase in place of ….to complete the following sentence:

The shape formed by the point A and the part of the line divided by A is called a…

A. Tia

B. Straight line

C. Score

D. Line segment

**Verse 2: **Choose the most suitable word or phrase in place of…. to complete the following sentence:

Any point M lying on the line xy is the common origin of…

A. two rays

B. two rays coincide

C. two opposite rays

D. straight line

**Question 3: **Name the rays in the following figure

A. Ox

B. Ox, Oy, Oz, Ot

C. Ox, Oy, Oz

D. xO, yO, zO, tO

**Question 4: **Let Ab and Ax be two parallel rays. Please choose the correct picture

**Question 5: **Given ray AB, let M belong to ray AB. Which of the following assertion is true?

A. M and A are on the same side of B

B. M and B are on the same side of A

C. A and B are on the same side of the US

D.M lies between A and B

**Question 6: **Given two opposite rays MA and Mb, X is a point on the ray MA. Which of the three points X, M, and B is between the other two points?

A. X

B. REMOVE

C. USA

D. Not yet concluded

**Verse 7: **In the following figure, how many rays are there?

A. 2

B. 0

C. 4

D. 1

**Verse 8: **Draw the figure according to the following expression:

+ Draw two distinct rays Ox, Oy that have the same origin but not opposite, not overlap

+ Draw a straight line aa’ intersecting two wagons Ox, Oy y in order at A and B (different from O)

+ Draw point C between two points A, B then draw Oz ray passing through C

How many distinct rays are obtained in the figure?

A. 6

B. 12

C. 9

D. 15

## 4. Conclusion

Through the lesson The line passes through these two points, you need to complete some of the objectives given by the lesson, such as:

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