Describe the series of transformations that have occurred 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 can perform a series of transformations. Let's break it down step by step:
1. Translation: We can translate the triangle in Quadrant IV upward to the same level as the triangle in Quadrant II. By moving the entire triangle vertically without changing its shape or orientation, we preserve congruence.
2. Reflection: After translating, we can reflect the translated triangle across the y-axis. This reflects the triangle over a vertical line, effectively swapping the left and right sides. The reflection doesn't change the shape or size of the triangle, so congruence is still maintained.
3. Rotation: Finally, we can rotate the reflected triangle counterclockwise around the origin by 180 degrees. This rotation flips the triangle upside down, effectively interchanging the top and bottom sides. Again, since rotation preserves shape and size, the resulting triangle is congruent to the original triangle in Quadrant IV.
By combining these three transformations (translation, reflection, and rotation), we can move the triangle in Quadrant IV to the triangle in Quadrant II while preserving congruence.