What is the main distinction between rigid and non-rigid transformations in geometry?

Rigid transformations preserve distance and angle measures, while non-rigid transformations change the size of figures but may preserve shape.

Fill in the blank: Under dilation, if a segment has length d and a scale factor k is applied, the length of the image segment becomes ___ .

K · d

True or False: Reflections preserve the orientation of a figure.

False. Reflections reverse orientation.

Riddle: I can move you across a plane without changing your shape, but I can change your size. What am I?

A dilation.

What property is preserved when a triangle undergoes a rigid transformation?

All three side lengths and angle measures are preserved, maintaining the triangle's area and perimeter.

Fill in the blank: If two lines are parallel in the pre-image, they will remain ___ in the image under any of the four main transformations.

Parallel

Describe how the concept of congruence is determined through transformations.

Two figures are congruent if one can be transformed into the other using only rigid transformations, which preserve distances and angles.

What happens to the area of a figure under a dilation with a scale factor of k?

The area is multiplied by k².

In a translation, what characteristics of a figure are preserved?

Distance, angle measure, parallelism, orientation, area, and perimeter are all preserved.

Fill in the blank: After reflecting a figure over a line, the distances from points to the line of reflection are ___ to the original distances.

Equal