To analyze the transformation of Triangle A into Triangle B, let's break down the steps:
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Rotation 180 degrees counterclockwise about the origin: This transformation maintains the shape and size of the triangle. The angles remain the same, as rotation does not affect the interior angles of any geometric figure.
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Translation 4 units to the right: A translation also maintains the shape and size of the triangle, including the measures of the angles.
Given these transformations, the following statements can be evaluated:
A. Triangle B has the same shape as Triangle A.
- This statement is true. Both rotation and translation preserve the shape of the triangle.
B. Triangle B has a different shape than Triangle A.
- This statement is false. Since the transformations do not change the shape, Triangle B retains the same shape as Triangle A.
C. The angles in Triangle B have the same measures as corresponding angles in Triangle A.
- This statement is true. The angles remain unchanged in size after a rotation and translation.
D. The angles in Triangle B have smaller measures than corresponding angles in Triangle A.
- This statement is false. The angles do not decrease in measure due to the transformations.
E. The angles in Triangle B have larger measures than corresponding angles in Triangle A.
- This statement is false. The angles remain unchanged and do not increase in measure.
Thus, the two true statements about Triangle B are:
- A. Triangle B has the same shape as Triangle A.
- C. The angles in Triangle B have the same measures as corresponding angles in Triangle A.
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