33
The broken line and its length
Textbook: Part 1, lesson 33, pp. 128–129
GoalDistinguish a broken line, a closed broken line and a polygon; find the length of a broken line.
New words
broken line · siniq chiziqlink (segment of a broken line) · bo‘g‘inpolygon · ko‘pburchakclosed broken line · yopiq siniq chiziq
Explanation
A figure made of segments joined one after another is called a broken line; the segments are its links (sides) and the segment ends are its vertices. The length of a broken line equals the sum of the lengths of its links. If its start and end coincide, it is a closed broken line. A closed broken line that does not cross itself is called a polygon. By the number of sides a polygon is a triangle, quadrilateral, pentagon, hexagon and so on. The sum of the side lengths of a polygon is its perimeter.
Worked examples
The links of broken line ABCD are AB = 5 cm, BC = 8 cm, CD = 6 cm. Its length is 5 + 8 + 6 = 19 cm.
A closed broken line with AB = 4 cm, BC = 6 cm, CD = 5 cm, DA = 7 cm forms a quadrilateral; its perimeter is 4 + 6 + 5 + 7 = 22 cm.
Class activity
“Drawing broken lines”: pupils draw a 5-link broken line in a squared notebook, measure each link with a ruler and find the total length.
Practice
1
A four-link broken line has a first link of 9 cm, and each next link is 2 cm longer than the one before. What is its length in cm?
48
2
A pentagon has sides 9, 11, 8, 12 and 10 cm. Find its perimeter (cm).
50
3
A four-link broken line is 31 cm long and three of its links are 7 cm each. How long is the fourth link (cm)?
10
4
Is a closed broken line that crosses itself a polygon? Why?
No: a polygon must be a closed broken line that does not cross itself.