Math 6 Chapter 1 Lesson 6: Line segment
1. Summary of theory Tóm
1.1. Straight line
The figure consisting of any two points A, B and all points lying between two points A and B is called the line segment AB.
1.2. Line length
Each line segment has a specified length, greater than 0.
If two points coincide, then we say that the distance between them is 0.
Two equal line segments have the same length.
On an origin O, for any number m > 0 there is always a point M so that OM = m.
On an Ox ray if there are two points M, N with OM = m, ON = n and m < n, then point M lies between two points O, N.
1.3. Add the length of the line segment
If point M lies between two points A and B, then we have AM + MB = AB.
And vice versa, if we have AM + MB = AB, then three points A, M, B are collinear and point M lies between two points A, B.
2. Illustrated exercise
Question 1: On the Ox ray there are three points A, B, C. Know OA = 15cm; OB = 24cm and OC = 19cm.
a. Prove AB = AC + CB.
b. Calculate the lengths of the line segments AB, AC, and CB and re-solve the proven relation in question a.
a. Since OA = 15; OB = 24; OC = 19 AO < OC < OB
⇒ Point C lies between two points A and B, so AC + CB = AB.
b. OA = 15; OB = 24 OA < OB
⇒ Point A is between two points O, B
OB = OA + AB
24 = 14 + AB
So AB = 9
Similarly, we can calculate AC = 4 and CB = 5
4 + 5 = 9 ⇒ AC + CB = AB.
Verse 2: On the Ox ray there are five points A, B, C, M, N. Know OA = 4cm, OB = 7cm, OC = 10cm, OM = 5cm and ON = 9cm.
a. Use a ruler to draw points A, B, C, M, N on the x-ray.
b. Prove that point M lies between two points A and B and point N lies between two points B and C.
c. Prove that point N lies between two points M and C.
b. We have OA < OM < OB, so M lies between A and B.
OB < ON < OC, so N lies between B and C.
c. We have OM < ON < OC so N should be between M and C.
Question 3: On the line x’x take a point O. On the x-ray there are two points A, B and on the x-ray there are two points C, D. Know OA = OC = 3cm and OB = OD = 5cm.
a. Prove AB = CD.
b. Prove AD = CB.
a. We have AB = OB – OA = 2cm
CD = OD – OC = 2cm
b. Point O belongs to line segment AD, so AD = AO + OD
⇒ AD = 3 + 5 = 8cm
Similarly, we have CB = 8cm.
Figure out what to prove.
3.1. Essay exercises
Question 1: On the X-ray, give three points A, B, M. Know OA = 8cm, OB = 16cm and AM = 5cm.
a. Calculate AB.
b. Calculate OM and MB.
Verse 2: Given four points A, B, C know AB = 18; AC = 12; DB = 3. Two points C and D belong to line segment AB.
a. Prove that point D lies between two points C and B and point C lies between two points D and A.
b. Calculate CB, CD.
3.2. Multiple choice exercises Bài
Question 1: Choose the most suitable word or phrase in place of…. to complete the following sentence:
The figure consisting of two points A and B and all the points between A and B are called….
A. line AB
B. line segment AB
C. ray AB
D. grade A
Verse 2: Choose the most suitable word or phrase in place of…. to complete the following sentence:
The figure consisting of the point O and the part of the line divided by the point O is called a….
A. the origin line O
B. line segment O
C. origin ray O
D. line O
Question 3: The teacher asked to “draw the line segment MN intersecting the line PQ”. The three friends Lan, Hung, and Hue draw as follows:
Ask who drew correctly?
D. All three of you are right
Question 4: Let I be any point of the line segment AB. Which of the following assertion true?
A. Score I must match A or B
B. Point I is between two points A and B
C. Point I either coincides with point A or lies between two points A and B or coincides with B
D. Point I must be different from A and B
Question 5: Name the lines shown in the figure below?
A. MN, MQ, NQ, ML, LP, MP, NP
B. MN, MQ, NQ, ML, LP, MP
C. MN, MQ, NQ, NP
D. MN, MQ, NQ, ML, LP
Question 6: Let G be a point on the line segment HK. Which of the three points G, H, and K lies between the other two points?
D. There is no point between the other two points
Verse 7: How many lines can be drawn through two distinct points?
D. Some others
Verse 8: Choose the most suitable word or phrase in place of…. to complete the following sentence:
Two points M, N are called….of the line segment MN
D. A and B are both correct
Verse 9: Through 4 non-collinear points, how many line segments can be drawn?
Question 10: For drawings
Which line segment does line xx’ intersect?
D. All 3 answers above
Question 11: For drawings
Let’s choose the ray that cuts the line segment AB.
B. Ox Ray’
C. Rays OA
D. Both B and C are correct
Verse 12: Draw 3 lines such that each line intersects the other two segments.
Which drawing is correct?
A. Figure 1
B. Figure 2
C. Figure 3
D. All 3 pictures are correct
Through the lecture, The line passes through these two points, you need to complete some of the objectives given by the lesson, such as: