Question

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Explanation:

1. First blank: $\boldsymbol{\overrightarrow{YZ} = \overrightarrow{YZ'}}$, because the center of dilation $Y$ stays fixed so the segment from $Y$ to itself and the ray from $Y$ to $Z$ maps directly to $Y Z'$.
2. Second blank: $\boldsymbol{\text{Point } Y}$, as the center of dilation remains unchanged through the transformation.
3. Third blank: $\boldsymbol{\text{angle measures}}$, dilations do not alter the size of angles.
4. Fourth blank: $\boldsymbol{\angle X'}$, since $\angle X \cong \angle A$ and dilation preserves angles.
5. Fifth blank: $\boldsymbol{AC}$, as the scale factor $\frac{AC}{XZ}$ maps $\overline{XZ}$ to a segment congruent to $AC$.
6. Sixth blank: $\boldsymbol{\text{ASA (Angle-Side-Angle)}}$, we have two pairs of congruent angles ($\angle Y \cong \angle B$, $\angle X' \cong \angle A$) and the included side $Y X'$ proportional/now congruent to $AB$.
7. Seventh blank: $\boldsymbol{\text{rigid transformations (translations/rotations/reflections)}}$, these map congruent figures onto each other.
8. Eighth blank: $\boldsymbol{\text{a dilation followed by rigid transformations}}$, combining the initial dilation and the rigid congruence mapping.

Answer:

1. $\boldsymbol{\overrightarrow{YZ} = \overrightarrow{YZ'}}$
2. $\boldsymbol{\text{Point } Y}$
3. $\boldsymbol{\text{angle measures}}$
4. $\boldsymbol{\angle X'}$
5. $\boldsymbol{AC}$
6. $\boldsymbol{\text{ASA}}$
7. $\boldsymbol{\text{rigid transformations}}$
8. $\boldsymbol{\text{dilation + rigid transformations}}$