• Students learn that when lines are translated they are either parallel to the given line, or the lines coincide.
• Students learn that translations map parallel lines to parallel lines.
Two lines are said to be parallel if they do not intersect.
Translations map parallel lines to parallel lines.
Given a line L and a point P not lying on L, there is at most one line passing through P and parallel to L.
1. Draw a line passing through point P that is parallel to line L. Draw a second line passing through point P that is parallel to line L, that is distinct (i.e., different) from the first one. What do you notice?
2. Translate line along the vector AB . What do you notice about L and its image L'?
3. Line L is parallel to vector AB . Translate line L along vector AB. What do you notice about L and its image, L'?
4. Translate line L along vector AB. What do you notice about L and its image, L'?
5. Line L has been translated along vector AB resulting in L'. What do you know about lines L and L'?
6. Translate L1 and L2 along vector DE. Label the images of the lines. If lines L1 and L2 are parallel, what do you know about their translated images?