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Line Segments

Line Segments. Information. Line segments. A line segment is part of a line that contains all points between and including two endpoints. B. A. The points A and B are the endpoints of the line segment. The line segment is named AB or BA.

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Line Segments

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  1. Line Segments

  2. Information

  3. Line segments A line segment is part of a line that contains all points between and including two endpoints. B A The points A and B are the endpoints of the line segment. The line segment is named AB or BA. How many points are there in a line segment? There are infinitely many points in a line segment. This means that no matter how close A and B are, there is always another point between them.

  4. Distance and length of segments Line segments have a length, which is the distance between the two endpoints. The length of AB is denoted AB. Distance can be measured using a ruler. On a coordinate axis, the distance between two points is the difference between coordinates of the endpoints. B A –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

  5. Congruence Segments are called congruent if they have the same length, e.g. AB = CD. Congruent segments are denoted using the symbol ≅, e.g., AB ≅CD. D E A B C –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Properties of congruence AB ≅AB reflexive: if AB ≅BC, thenBC ≅AB symmetric: if AB ≅BC and BC ≅CD, thenAB ≅CD transitive:

  6. Equipment needed for constructions Which equipment do you need for constructing line segments? ruler protractor sharp pencil compass

  7. Constructing a line segment

  8. Segment addition postulate and midpoint The segment addition postulate: if B is between A and C then: AB + BC=AC A B C The midpoint, M, of a line segment is the point that bisects, or equally divides, a line segment into two congruent line segments: AM≅ MC, which means AM = MC. A M C In figures, congruent segments are denoted with tick marks.

  9. Congruent segments

  10. Segment addition postulate Ashley and Corinne live 21 blocks apart on the same street. Brian lives between them and 7 blocks away from Ashley. How far apart do Brian and Corinne live? 1. Represent the street as a line, with points representing where the children live: A B C 2. Translate the information given into line segment lengths: AC=21 AB=7 3. Substitute the values into the segment addition postulate to find the answer: AB + BC = AC segment addition postulate: 7 + BC = 21 substitute: BC = 21 – 7 =14 rearrange and solve:

  11. Summary activity

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