Math 6 Chapter 1 Lesson 7: Length of line segment
1. Summary of theory
1.1. Line length
Each line segment has a length. The length of the line segment is a number greater than 0.
1.2. Compare two line segments
We can compare two line segments by comparing their lengths.
Suppose we have: AB = 3cm, CD = 3cm, EG = 4cm
Two line segments AB and CD are equal or have the same length and denoted AB = CD.
The line EG is longer (greater than) the line CD and the symbol EG > CD.
Line segment AB is shorter (smaller than) segment EG and denoted AB < EG.
2. Illustrated exercise
Question 1: Choose the word or phrase: (1) the same; (2) 0; (3) line length; (4) the distance between two points; (5) ways, fill in the appropriate blank in each of the following sentences to correctly express the length of the line.
a. AB = 2 (cm) also say ….. A and B equal 2 (cm) or say…. AB equals 2 (cm) or A …..B an interval equal to 2 (cm).
b. Two points A and B coincide also say that ….A and B are equal to …. or A …… B an interval equal to ….. or …… AB equal to…..
c. AB = 0 also says that ……A and B are equal to …… or two points A and B ….. or …… AB is equal to ….. or A …..b is an interval equal to…..
a. AB = 2 (cm) also says …(4) distance between two points.. A and B is equal to 2 (cm) or say…(3) length of line… AB is equal to 2 (cm) or A …(5) is a distance of… B by a distance of 2 (cm).
b. Two points A and B coincide are also said to be …(4) the distance between two points… A and B is equal to …(2) 0… or A …(5) is a distance from… B equal to …(2) 0… or …(3) length of line segment… AB is equal to…(2) 0…
c. AB = 0 also says that …(4) the distance between two points… A and B is equal to…(2) 0… or two points A and B…(1) coincide…or…(3) length of line segment… AB is equal to…(2) 0…or A …(5) distance from… B is equal to…(2) 0…
Given AB = 5(cm) and CD = 3 (cm), EF = 4 (cm) and GH = 3 (cm).
Select word, phrase or symbol: greater than; less; equal; of the same length; <; =; >, fill in the blank (…)
a. AB …..CD or CD …..AB or AB…. CD or CD …..AB.
b. CD and GH……or CD and GH……or CD……GH
c. AB……EF or EF……AB or AB……EF or EF……AB
a. AB is greater than CD or CD is less than AB or AB > CD or CD < AB.
b. CD and GH are equal, or CD and GH are the same length, or CD = GH.
c. AB is greater than EF or EF is less than AB or AB > EF or EF.
Question 3: Choose one of the symbols < or = or > to fill in the blanks (…) below to properly represent the comparison of the lengths of the line segments.
3.1. Essay exercises
Question 1. Arrange the lengths of the line segments AB, BC, AC in ascending order
Verse 2. For drawings
a) Arrange the lengths of the line segments AB, BC, CD, AD in descending order.
b) Calculate the perimeter of the figure ABCD.
3.2. Multiple choice exercises
Question 1: Choose the correct figure according to the following expression:
Draw line segment AB without intersecting line CD but line AB intersecting line CD
Verse 2: On the X-ray give 4 points A, B, C, D. Know that A lies between two points B and C; point B lies between two points C and D. Know OA = 7cm, OD = 3cm, BC = 8cm, AC = 3BD. Calculate the length AC
Question 3: Let 4 points A, B, M, N lie on the line d. Point M lies between two points A and N; Point N lies between two points M and B. Know AN = 6cm, MN = 2.5cm, NB = 2AM. Calculate the length AB
Question 4: Given 20 points of which no 3 points are collinear. Assume that every two points are connected by a straight line. How many lines can be drawn in all?
Question 5: Given n distinct points. Every two points we draw a straight line. Of the n points, no 3 points are collinear. Calculate n can draw 276 lines.
Question 6: Given 45 line segments in which each line segment intersects the remaining line segments, no 3 lines are concurrent. Calculate the number of intersections?
Verse 7: Choose the most correct answer. On the Ox ray draw the lines OR, OS such that OR = 3cm, OS = 6cm. Then:
A. OR = RS
B. RS = 3cm
C. R is between O and S
D. All 3 answers above are correct
Verse 8: Let E be the point between the two points I and K. Know that IE = 4cm, EK = 10cm. Calculate the length of the line segment IK
Verse 9: Let I be a point r of the line segment MN. When IM = 4cm, MN = 7cm, what is the length of line segment IN?
Question 10: On the line a take 4 points M, N, P, Q in that order. Let MN = 2cm, MQ = 5cm and NP = 1cm. Find pairs of equal line segments
A. MP = PQ
B. MP = NQ
C. MN = PQ
D. Both B and C are correct
Question 11: On the X-ray, take two points M, N such that OM = 3cm and point N such that ON = 7cm. Take point P such that MP = 2cm. Calculate PN
A. 6cm or 2cm
B. 6cm or 3cm
C. 5cm or 2cm
D. 6cm or 4cm
Through this lesson on Line length, you need to complete some of the objectives given by the lesson, such as: