Question
(1 point)
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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 #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise).
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 .
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Answered by
GPT-4o mini
The statements regarding the congruence of the trapezoids based on the transformations applied to figure ABCD include:
1. **Translation** (Statement #2): This transformation moves the figure without changing its size or shape, hence the trapezoids would be congruent.
2. **Rotation** (Statement #4): A 90° counterclockwise rotation also preserves the shape and size, leading to congruence.
3. **Rotation** (Statement #3): Similarly, a 270° (which is equivalent to a 90° clockwise rotation) would maintain congruence for the same reason.
4. **Reflection** (Statement #1): Reflecting over the line y=x would also produce a congruent figure, as reflections maintain distance and angles.
All four statements indicate congruence, but it's important to note that statements #3 and #4 describe different rotations and one of them wouldn't apply simultaneously, but each transformation mentioned does indeed lead to congruence of the trapezoids. If you're looking for which statements are true regarding congruence, all statements are valid methods to show that the trapezoids remain congruent after the respective transformations are applied.
1. **Translation** (Statement #2): This transformation moves the figure without changing its size or shape, hence the trapezoids would be congruent.
2. **Rotation** (Statement #4): A 90° counterclockwise rotation also preserves the shape and size, leading to congruence.
3. **Rotation** (Statement #3): Similarly, a 270° (which is equivalent to a 90° clockwise rotation) would maintain congruence for the same reason.
4. **Reflection** (Statement #1): Reflecting over the line y=x would also produce a congruent figure, as reflections maintain distance and angles.
All four statements indicate congruence, but it's important to note that statements #3 and #4 describe different rotations and one of them wouldn't apply simultaneously, but each transformation mentioned does indeed lead to congruence of the trapezoids. If you're looking for which statements are true regarding congruence, all statements are valid methods to show that the trapezoids remain congruent after the respective transformations are applied.