differentiating between figure A-D which transformation fails to preserve congruence
To differentiate between figure A-D and determine which transformation fails to preserve congruence, we need to analyze each figure and identify if any transformation changes the shape or size of the original figure.
Figure A: A triangle with side lengths 3, 4, and 5.
Figure B: A rectangle with side lengths 4 and 6.
Figure C: A square with side length 5.
Figure D: A parallelogram with side lengths 3 and 6.
Now, let's consider each transformation:
1. Translation: This transformation involves sliding the figure without changing its shape or size. Translation preserves congruence.
2. Reflection: This transformation involves flipping the figure over a line. Reflection preserves congruence.
3. Rotation: This transformation involves turning the figure around a point. Rotation preserves congruence.
4. Dilation: This transformation involves changing the size of the figure while keeping the shape. If the scale factor is the same for all sides, the congruence is preserved. However, if the scale factor is different for different sides, the congruence is not preserved.
Based on these principles, let's determine which transformation fails to preserve congruence for each figure:
Figure A: None of the transformations (translation, reflection, rotation, or dilation) fail to preserve congruence.
Figure B: None of the transformations (translation, reflection, rotation, or dilation) fail to preserve congruence.
Figure C: None of the transformations (translation, reflection, rotation, or dilation) fail to preserve congruence.
Figure D: The dilation transformation fails to preserve congruence if the scale factor is different for different sides. However, if the scale factor is the same for both sides, congruence is preserved.
Therefore, for figure D, the dilation transformation is the one that fails to preserve congruence if the scale factor is different for different sides.