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.
translation, then transformation
reflection, then translation
rotation, then translation
translation, then reflection
The correct answer is: translation, then reflection.
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 is a translation, followed by a reflection.
1. First, perform a translation by moving the triangle in Quadrant IV directly upward or downwards to a new position so that the corresponding vertices of the two triangles coincide. This translation ensures that the corresponding sides and angles of the two triangles coincide.
2. After the translation, perform a reflection across the y-axis to flip the triangle in Quadrant II. This reflection helps to align the triangles, ensuring that the corresponding sides and angles are congruent.
By performing the translation and reflection, the two triangles will eventually be in the same position and orientation, proving they are congruent.