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 to show that they are congruent, the following sequence of steps can be followed:
Step 1: Identify the coordinates of the vertices of the triangle in Quadrant IV. Let's assume the vertices of this triangle are (x1, y1), (x2, y2), and (x3, y3).
Step 2: Determine the translation vector that will move the triangle from Quadrant IV to Quadrant II. This translation vector can be calculated by taking the negative value of the x-coordinate of any vertex in Quadrant IV and adding it to the x-coordinate of the corresponding vertex in Quadrant II. Similarly, the y-coordinate of the vertex in Quadrant II will be the sum of the negative y-coordinate of the vertex in Quadrant IV and the appropriate constant.
Step 3: Apply the translation vector to each vertex of the triangle in Quadrant IV. To do this, add the x-component of the translation vector to the x-coordinates of the vertices, and add the y-component of the translation vector to the y-coordinates of the vertices.
Step 4: The result of applying the translation vector to the vertices of the triangle in Quadrant IV will give the coordinates of the vertices of the triangle in Quadrant II.
Step 5: To show that the two triangles are congruent, compare the lengths of the sides of the two triangles and the measures of the angles between these sides. If all corresponding sides and angles are equal, then the triangles are congruent.
Note: It's important to ensure that the translation vector is accurately calculated and applied to each vertex to ensure the triangles are translated correctly. Additionally, verifying the congruence by comparing the side lengths and angles is crucial to confirm that the triangles are truly congruent.