Question

triangle bac was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle xyz. based on these transformations, which statement is true?
options:
∠z ≅ ∠a
∠b ≅ ∠y
∠a ≅ ∠x
∠c ≅ ∠z

Explanation:

Step1: Recall the properties of rotation and dilation

Rotation and dilation are similarity transformations. Similar triangles have congruent corresponding angles.

Step2: Analyze each option

• For $\angle A\cong\angle X$: After rotation and dilation, $\angle A$ and $\angle X$ are not corresponding angles.
• For $\angle B\cong\angle Y$: After rotation and dilation, $\angle B$ and $\angle Y$ are not corresponding angles.
• For $\angle Z\cong\angle A$: After rotation and dilation, $\angle Z$ and $\angle A$ are not corresponding angles.
• For $\angle C\cong\angle Z$: Since rotation and dilation are similarity - preserving transformations, and $\angle C$ and $\angle Z$ are corresponding angles (because of the way the triangles are related by the transformation), they are congruent.

Answer:

$\angle C\cong\angle Z$