## Math 6 Chapter 1 Lesson 8: When is AM + MB = AB?

## 1. Summary of theory

If point M lies between two points A and B then AM + MB = AB. Conversely, if AM + MB = AB, then point M lies between two points A and B.

## 2. Illustrated exercise

**Question 1:** Let M points lie between A and B. Know AM = 3cm, AB = 8cm. Calculate MB.

**Solution guide:**

Since M lies between A and B, AM + MB = AB

Replace AM by 3cm, AB by 8cm, we have:

3 + MB = 8

MB= 8 – 3

MB = 5 (cm).

**Verse 2: **Draw arbitrarily three points A, B, C in a straight line. How to measure only 2 times and know the length of the line segments AB, BC, CA.

**Solution guide:**

Take three arbitrary points A, B, C on a certain line. You can measure AB, AC and then deduce BC, or measure BC, AC and then deduce AB, or measure AB, BC and then deduce AC.

**Question 3: **Let the line segment AB have length 11 cm. Point M lies between A and B. Know that MB – MA = 5cm. Calculate the lengths of the line segments MA, MB.

**Solution guide:**

MA + MB = 11 (cm) (1)

MB – MA = 5 (cm) (2)

From (1) and (2) deduce MB = 8cm, MA = 3cm.

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Let three points A, B, C be collinear. Which point lies between the other two if:

a. AC + CB = AB

b. AB + BC = AC

c. BA + AC = BC

**Verse 2: **Given three points A, B, M know AM = 3.7cm, MB = 2.3cm, AB = 5cm. Prove that:

a. Of the three points A, B, and M, none of them lies between the other two points.

b. Three points A, B, M are not collinear.

### 3.2. Multiple choice exercises

**Question 1: **If point P lies between two points M and N, then

A. PN + MN = PN

B. MP + MN = PN

C. MP + PN = MN

D. MP – PN = MN

**Verse 2: **If a line segment intersects a ray, how many points do the line segment and ray have in common?

A. 1

B. 2

C. 0

D. countless

**Question 3: **Let two points A and B lie on the ray Ox such that OA = 6cm, OB = 2cm. Which of the three points O, A, and B is between the other two points?

A. Score O

B. DISCLAIMER

C. Grade A

D. There is no point between the other two points

**Question 4: **Let O be the point between the two points A and B. The point I lies between the two points O and B. Choose the correct sentence.

A. Point O lies between two points A and I

B. Point A is between two points I and B

C. Point I is between two points A and B

D. Both A and C are correct

**Question 5: **Given 10 distinct points in which no three points are collinear, every two points we draw a line. How many lines are drawn in all?

A. 10

B. 90

C. 40

D. 45

**Question 6: **Given n distinct points \(\left( {n \ge 2,n \in N} \right)\) where no three points are collinear. Draw line segments say two of those n points. There are 28 lines in all. Look for n

A. n = 9

B. n = 7

C. n = 8

D. n = 6

**Verse 7: **Know AB = 7cm, CD = 5cm, MN = 6cm, PQ = 5cm. Compare line segment CD and line segment PQ

A. CD > PQ

B. CD < PQ

C. CD = PQ

D. Not comparable

**Verse 8: **How many lines does the line x’y’ intersect in the following figure?

A. 3

B. 4

C. 5

D. 6

**Verse 9: **Let the line segments AB = 4cm, MN = 5cm, EF = 3cm, PQ = 4cm, IK = 5cm. Choose the wrong answer

A. AB < MN

B. EF < IK

C. AB = PQ

D. AB = EF

**Question 10: **Given three points O, A, B such that OA = 2cm, OB = 3cm, AB = 5cm. Which statement below is true?

A. Point A lies between two points O and B

B. Point O lies between two points A and B

C. Point B is between two points O and A

D. Three points O, A, B are not collinear

**Question 11: **On the line d take 4 points A, B, C, D such that AB = 5cm, BC = 3cm, CD = 7cm. Calculate the length of AD given that B lies between C and D; C lies between A and B

A. AD = 15cm

B. AD = 9cm

C. AD = 5cm

D. AD = 1cm

**Verse 12: **Let MN = 12cm, MP = 4cm, PN = 8cm. Which point lies between the other two points?

A. US point

B. Female Score

C. Score P

D. No point in between

## 4. Conclusion

Through the lecture When is AM + MB = AB? Here, you need to accomplish some of the goals that the lesson gives, such as:

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