describe the sequence of steps used to move the triangle in quadrant IV to the triangle in quadrant II to show that the triangles are congruent
To move the triangle in Quadrant IV to the triangle in Quadrant II, we need to do a series of transformations while preserving the congruency of the triangles. Here is the sequence of steps to achieve this movement:
1. Start with the triangle in Quadrant IV, which we'll call Triangle ABC. Triangle ABC is defined by its three vertices, A, B, and C.
2. The first step is to reflect Triangle ABC over the y-axis. This means that we move every point of the triangle, A, B, and C, to the opposite side of the y-axis while keeping the distances from the y-axis the same. Let's call the new triangle after the reflection Triangle A'B'C'.
3. After the reflection, the two triangles, Triangle ABC in Quadrant IV and Triangle A'B'C' in Quadrant II, have the same size and shape but opposite orientations. They are congruent.
Therefore, the sequence of steps to move the triangle in Quadrant IV to the triangle in Quadrant II and show that the triangles are congruent is to reflect the triangle over the y-axis.