Question

triangle $\triangle abc$ is the result of translating $\triangle abc$ by 6 units to the right and 2 units down.

image of coordinate plane with triangle abc

select all of the correct statements about the unchanged properties of $\triangle abc$ and $\triangle abc$.

choose all answers that apply:

a $\angle a$ and $\angle a$ have the same measures.

b $b$ and $b$ have the same coordinates.

c the areas of $\triangle abc$ and $\triangle abc$ are the same.

d none of the above

Explanation:

Step1: Recall Translation Properties

Translation is a rigid transformation, so it preserves shape, size, angles, and area.

Step2: Analyze Option A

Angles are preserved in translation, so \( \angle A \) and \( \angle A' \) have the same measure. This is correct.

Step3: Analyze Option B

Translation moves the figure, so coordinates of \( B \) and \( B' \) will differ (translated 6 right, 2 down). This is incorrect.

Step4: Analyze Option C

Area is preserved in rigid transformations (translation), so areas of \( \triangle ABC \) and \( \triangle A'B'C' \) are the same. This is correct.

Step5: Analyze Option D

Since A and C are correct, D is incorrect.

Answer:

A. \( \angle A \) and \( \angle A' \) have the same measures.
C. The areas of \( \triangle ABC \) and \( \triangle A'B'C' \) are the same.