Congruent figures practice

Question

The first step to determine that the rectangle in quadrant ||| is confetti the rectangle in quaadrant | was to rotate the first rectangle 90 degrees clockwise about the origin what is the next step

Answer 1

To determine if the rectangle in quadrant III is congruent to the rectangle in quadrant I after rotating the first rectangle 90 degrees clockwise about the origin, the next step would typically involve comparing the dimensions and positions of the rectangles after rotation.

Here's a step-by-step approach:

1. Rotation Confirmation: Verify the coordinates of the rectangle in quadrant III after the 90-degree clockwise rotation. If the original rectangle has vertices at \((x, y)\), then the new coordinates after rotation will be \((y, -x)\).

2. Identify Dimensions: Calculate the dimensions (length and width) of both rectangles. Congruent figures have equal dimensions.

3. Position Check: Analyze the positions of the rectangles. After the rotation, ensure that the rectangle in quadrant III matches in size and shape to the rectangle in quadrant I.

4. Reflection (if required): If needed, you can reflect the rectangle in quadrant III across the appropriate axis to see if it overlaps or matches the rectangle in quadrant I.

5. Final Comparison: If both the dimensions and shapes match after any necessary transformations, you can conclude that the rectangles are congruent.

In summary, the next step involves confirming the new coordinates of the rotated rectangle and then comparing dimensions and positions to establish congruency.