1. Problem: Determine if two line segments or two angles can be similar. 2. Two line segments are similar if they have the same shape and their lengths are proportional. Since line segments are one-dimensional, similarity means their lengths have a constant ratio. 3. Two angles are always similar because similarity for angles means having the same measure. Angles with the same measure are congruent and thus similar. 4. Problem: Figure G' is the image of Figure G by a dilation. 5. The center of dilation is the point from which all points of the figure are expanded or contracted. In the graph, point C is the center because lines connect C to corresponding points on G and G'. 6. To estimate the scale factor, measure the distance from C to a point on G and from C to the corresponding point on G'. The scale factor $k$ is given by: $$k = \frac{\text{distance from } C \text{ to } G'}{\text{distance from } C \text{ to } G}$$ 7. Since G' is closer to C than G, the scale factor $k$ is less than 1, indicating a reduction. 8. For example, if $CG = 6$ units and $CG' = 3$ units, then: $$k = \frac{3}{6} = 0.5$$ This means the figure is scaled down by a factor of 0.5 from point C. Final answers: a. The center of dilation is point C. b. The scale factor is approximately 0.5 (or the ratio of distances from C to G' and G).