Question

1. transformations such as translations, reflections, and rotations do not alter the _____________ and shape of a figure.
2. a transformation that changes the size of a figure but not its shape is called _____________.
3. to verify that two figures are congruent, the lengths of their corresponding _____________ must be equal.
4. reflecting a point over the line $y = x$ involves swapping its _____________.
5. reflecting a figure over the y-axis changes the sign of its _____________ coordinates.

Explanation:

1. Rigid transformations (translations, reflections, rotations) preserve both the size and shape of a figure, so they do not alter these properties.
2. A dilation is the specific transformation that scales a figure (changes its size) while keeping its shape consistent.
3. Congruent figures have all corresponding sides of equal length, so verifying this equality confirms congruence.
4. The line $y=x$ is a line of reflection where each point $(x,y)$ maps to $(y,x)$, requiring a swap of the x and y coordinates.
5. Reflecting over the y-axis transforms a point $(x,y)$ to $(-x,y)$, which only changes the sign of the x-coordinate.

Answer:

1. size
2. dilation
3. sides
4. x and y coordinates
5. x