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.
1. Begin by labeling the vertices of both triangles. Let the vertex of the triangle in Quadrant IV be A, the vertex in Quadrant II be B, and the remaining vertices C and D in both triangles.
2. Note that the corresponding angles B and D in each triangle are congruent, as they both form a right angle.
3. Determine the length of side AD in the triangle in Quadrant IV. For example, let's say AD measures 5 units.
4. Use a straightedge to draw a line segment AB starting from vertex A and extending to Quadrant II. The length of AB should be equal to the length of AD, which in this case is 5 units.
5. At vertex B, draw a perpendicular line segment BC that intersects the x-axis in Quadrant II. Ensure that the length of BC is the same as the length of AD, which is 5 units in this example.
6. Connect the endpoints C and D to form triangle ABC in Quadrant II.
7. By construction, we have created two congruent triangles. Triangle ADC in Quadrant IV is congruent to triangle ABC in Quadrant II. This can be justified by the fact that they share a common side AD and corresponding angles B and D are congruent.
Therefore, the sequence of steps would involve establishing the congruence between the triangles by creating identical side lengths and corresponding angles using straightedge constructions.