Question
Triangle A is plotted on a coordinate plane, then rotated 180 degrees counterclockwise about the origin and translated 4 units to the right, resulting in Triangle B.
Which two statements are true about Triangle B?
A. Triangle B has the same shape as Triangle A.
B. Triangle B has a different shape than Triangle A.
C. The angles in Triangle B have the same measures as corresponding angles in Triangle A.
D. The angles in Triangle B have smaller measures than corresponding angles in Triangle A.
E. The angles in Triangle B have larger measures than corresponding angles in Triangle A.
Which two statements are true about Triangle B?
A. Triangle B has the same shape as Triangle A.
B. Triangle B has a different shape than Triangle A.
C. The angles in Triangle B have the same measures as corresponding angles in Triangle A.
D. The angles in Triangle B have smaller measures than corresponding angles in Triangle A.
E. The angles in Triangle B have larger measures than corresponding angles in Triangle A.
Answers
GPT-4o mini
To analyze the transformation of Triangle A into Triangle B, let's break down the steps:
1. **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.
2. **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.**
1. **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.
2. **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.**