Describe the series of Transformations that have occurred to move the triangle and quadrant for to the triangle in quadrant 2 to show that the triangles are congruent
To move the triangle in quadrant 2 to the triangle in quadrant 4 so that they are congruent, the following series of transformations will be applied:
1. Translation: Move the triangle horizontally to the right so that its horizontal base coincides with the x-axis. This translation ensures that the horizontal distance between the two triangles is the same.
2. Reflection: Reflect the translated triangle over the y-axis. This reflection ensures that the two triangles have the same horizontal orientation.
3. Rotation: Rotate the reflected triangle 180 degrees counterclockwise around the origin. This rotation ensures that the two triangles have the same overall shape and orientation.
4. Translation: Move the rotated triangle horizontally to the left, aligning its horizontal base with the x-axis in quadrant 4. This translation ensures that the triangles have the same horizontal position.
After these transformations, the triangle in quadrant 2 and the triangle in quadrant 4 will be congruent, as all corresponding angles and sides will be equal.