Point in the middle. Midpoint of line segment

### 1.1. Knowledge to remember

#### 1.1.1. Point in the middle

A, O, B are three collinear points.

O is the point in between two points A and B.

#### 1.1.2. Midpoint of line segment

M is the midpoint between the two points A and B

The length of line segment AM is equal to the length of line segment MB

Write: AM = BM

M is called the midpoint of line segment AB.

### 1.2. Solving Textbook Exercises

**Lesson 1: **In the picture below

a) What are the three collinear points?

b) M is the midpoint between which two points?

N is the point in between which two points?

O is the point in between which two points?

__Solution guide:__

- Identify 3 points lying on the same line segment in the given figure.
- Observe the figure and then determine the lying point M; N; O lies between any two points.

a) A, M, B are three collinear points

M, O, N are three collinear points

C, N, D are three collinear points

b) M is the point in between two points A and B.

N is the point between the two points C and D.

O is the midpoint between the two points M and N.

**Lesson 2:** Which sentence is correct and which is wrong?

a) O is the midpoint of the line segment AB

b) M is the midpoint of line segment CD.

c) H is the midpoint of line segment EG.

d) M is the point in between the two points C and D.

e) H is the point between the two points E and G.

__Solution guide:__

- Recall knowledge of midpoints and midpoints of a line segment to determine whether a given statement is true or false.
- If O is the midpoint of line segment AB, then:
- O lies between two points A and B.
- Length of line segment AO = OB.

__Solution guide:__

a) Right

b) Wrong. Because M is not yet between the two points C and D.

c) Wrong. Because the length of the line segment EH is different from the length of the line segment HG.

d) Wrong. Because of the three A’s; M; D is not aligned.

e) Right

**Lesson 3:** Name the midpoints of the line segments BC, GE, AD, IK.

__Solution guide:__

- Recall knowledge of the midpoint of a line segment to find the solution.
- If M is the midpoint of line segment AB, then:
- M lies between two points A and B.
- Length of line segment AM = MB.

I is mid point of line segment BC (because B, I, C are collinear and BI = IC)

K is the midpoint of line segment GE (because G, K, E are collinear and GK = KE)

O is the midpoint of line segment AD (because A, O, D are collinear and AO = OD)

O is the midpoint of line segment IK (because I, O, K are collinear and IO = OK).

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