Question
(1 point)
Responses
Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units
Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units
Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
Statement #1: The trapezoids are congruent because ABCD was reflected over the line y=x .
Statement #1: The trapezoids are congruent because ABCD was reflected over the line y=x .
Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
Answers
GPT-4o mini
To evaluate the statements about the congruence of the trapezoids based on the transformations mentioned, we need to consider the effects of each transformation on the shape of the trapezoids.
1. **Statement #1**: The trapezoids are congruent because ABCD was reflected over the line y=x.
- **Analysis**: Reflection across a line maintains the shape and size of the figure. Thus, if ABCD is reflected over the line y=x, the resulting trapezoid will be congruent to ABCD. **This statement is true.**
2. **Statement #2**: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
- **Analysis**: Translation, like reflection, also maintains the shape and size of the figure. Therefore, the resulting trapezoid after this translation will be congruent to ABCD. **This statement is true.**
3. **Statement #3**: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
- **Analysis**: Rotation is another transformation that preserves the shape and size of the figure. A 270° rotation (which is equivalent to a 90° rotation clockwise) will also result in a trapezoid congruent to ABCD. **This statement is true.**
4. **Statement #4**: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
- **Analysis**: Similar to statement #3, a 90° rotation (counterclockwise) also preserves shape and size. Thus, the resulting trapezoid will be congruent to ABCD. **This statement is true.**
In conclusion, all four statements accurately describe transformations that would result in congruent trapezoids.
1. **Statement #1**: The trapezoids are congruent because ABCD was reflected over the line y=x.
- **Analysis**: Reflection across a line maintains the shape and size of the figure. Thus, if ABCD is reflected over the line y=x, the resulting trapezoid will be congruent to ABCD. **This statement is true.**
2. **Statement #2**: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units.
- **Analysis**: Translation, like reflection, also maintains the shape and size of the figure. Therefore, the resulting trapezoid after this translation will be congruent to ABCD. **This statement is true.**
3. **Statement #3**: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise).
- **Analysis**: Rotation is another transformation that preserves the shape and size of the figure. A 270° rotation (which is equivalent to a 90° rotation clockwise) will also result in a trapezoid congruent to ABCD. **This statement is true.**
4. **Statement #4**: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
- **Analysis**: Similar to statement #3, a 90° rotation (counterclockwise) also preserves shape and size. Thus, the resulting trapezoid will be congruent to ABCD. **This statement is true.**
In conclusion, all four statements accurately describe transformations that would result in congruent trapezoids.