Question

measurement and construction
given △abc with horizontal base $overline{ab}$ extended (dashed line) and another horizontal reference - line drawn at c, translate △abc in the direction of $overline{ef}$ a distance of ef. use your compass to help with the direction. use your protractor to help with distance.

1. in the diagram below, △efg is a transformation of △efg.

(a) using tracing paper, are the two triangles the same shape and size?
(b) could △efg be the image of △efg after a translation alone? support your answer with measurements.
problem solving

1. which of the following is a property of translations that is not also a property of other types of rigid motions?

(1) they map line segments to other line segments of equal length
(2) they map angles to other angles of the same size
(3) they map lines to parallel lines
(4) they map lines to perpendicular lines

Explanation:

Step1: Recall properties of translations

A translation is a rigid - motion that slides a figure. It preserves length, angle measure, and parallelism.

Step2: Analyze each option

• Option (1): Other rigid motions like rotations and reflections also map line - segments to equal - length line - segments.
• Option (2): Rotations and reflections also map angles to equal - measure angles.
• Option (3): Translations map lines to parallel lines. Rotations and reflections do not always do this. For example, a rotation will change the orientation of a line and a reflection can map a line to a non - parallel line.
• Option (4): Translations do not map lines to perpendicular lines.

Answer:

(3) they map lines to parallel lines