☰ Contents · Geometry

Length of a segment and measuring

Lessons 5–6 · 2 lessons · Geometry Grade 7, corrected and expanded 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2017 (approved by the Ministry of Public Education)
5

Length of a segment and its properties

Textbook: pp. 14–15
GoalUse the idea of length and the property AC = AB + BC.
New words
unit segment · birlik kesmalength of a segment · kesmaning uzunligisum of segments · kesmalar yig‘indisidistance · masofa
Explanation

To measure, we choose one segment and call it the unit segment (length 1). We lay the unit segment (and, if needed, its fractions) along the given segment one after another and count how many fit; the positive number we get is the length of the segment. Every segment has a definite positive length, and equal segments have equal lengths. The main property (accepted without proof): if B lies between A and C on a line, then AC = AB + BC. From it come addition and subtraction of segments: for example, if B lies on segment AC, then BC = AC − AB. The distance between A and B equals the length of segment AB.

Worked examples
A, B, C lie on a line, B between A and C, AB = 6 cm, BC = 10 cm; then AC = 6 + 10 = 16 cm.
If AB = 6 cm and BC = 10 cm but the order is unknown, AC may be 16 cm or 10 − 6 = 4 cm (when A is between B and C).
Class activity

“Measure with string”: mark a string at two places and compare the pieces: do the lengths of the pieces add up to the whole string?

Practice
1
B lies between A and C. AB = 7 cm, BC = 12 cm. Find AC (cm).
2
AC = 30 cm, AB = 11 cm, B between A and C. Find BC (cm).
3
A, B, C on a line, AB = 4, BC = 9. Find the two possible values of AC.
4
Why is AC = AB + BC not always true if the three points are not on one line?