Which of the following is NOT true of a trapezoid that has been reflected across the x-axis
To determine which of the following is NOT true of a trapezoid that has been reflected across the x-axis, you need to understand what happens to the shape when it undergoes a reflection.
When a shape is reflected across the x-axis, all of the y-coordinates of its vertices are multiplied by -1. In other words, if a vertex has coordinates (x, y), after the reflection it will have coordinates (x, -y).
Now we can consider the characteristics of a trapezoid and see which one does not hold true after reflection across the x-axis.
1. The shape remains a trapezoid: This statement is true. A trapezoid is defined as a quadrilateral with one pair of parallel sides. Reflection across the x-axis preserves the parallelism of the sides, so the shape will still be a trapezoid.
2. The shape becomes congruent to the original: This statement is not true. When a shape is reflected, it does not become congruent (i.e., identical) to the original shape, unless it is reflected onto itself.
3. The orientation of the shape is reversed: This statement is true. Reflection across the x-axis flips the shape vertically, reversing its orientation.
4. The angles of the shape remain the same: This statement is not true. Reflection across the x-axis changes the angles of the trapezoid. The acute angles become obtuse, and the obtuse angles become acute.
Therefore, the correct answer is: The shape becomes congruent to the original.