Which of the following statements is true of all translations?
A.
all corresponding sides in a figure and its translation are parallel or lie on the same line
B.
all angle measures increase
C.
all corresponding vertex positions in a figure and its translation remain the same
D.
all side positions remain the same
The correct answer is C. All corresponding vertex positions in a figure and its translation remain the same.
In a translation, the figure is moved without changing its shape or size. The position of each vertex is shifted by the same amount and in the same direction. Therefore, the corresponding vertex positions in the original figure and its translation will remain the same.
The correct statement among the options is:
A. all corresponding sides in a figure and its translation are parallel or lie on the same line
To determine which statement is true of all translations, let's examine each option:
A. All corresponding sides in a figure and its translation are parallel or lie on the same line:
This statement is true in a translation. When a figure is translated, all corresponding sides in the original figure and its translation are parallel to each other, meaning they never intersect. So, option A is a true statement.
B. All angle measures increase:
This statement is not true of all translations. In a translation, the size of angles remains the same. Translations only change the position of the figure, not the measurements of the angles. Therefore, option B is incorrect.
C. All corresponding vertex positions in a figure and its translation remain the same:
This statement is not true of all translations. In a translation, the position of every point in the figure is shifted in the same direction and distance. The individual vertex positions change, but their corresponding relationships remain consistent. So, option C is incorrect.
D. All side positions remain the same:
This statement is not true of all translations. In a translation, the position of every point in the figure is shifted in the same direction and distance. This means that the side positions also change. So, option D is incorrect.
In conclusion, the only statement that is true for all translations is option A: all corresponding sides in a figure and its translation are parallel or lie on the same line.