To determine what transformations would not result in two quadrilaterals being congruent, we first need to understand the types of transformations that can create congruence.
Transformations that preserve the shape and size of a figure (and thus can result in congruent figures) include:
- Translation - Moving the figure without rotation or reflection.
- Rotation - Turning the figure around a point.
- Reflection - Flipping the figure over a line.
However, there are certain transformations that would not result in congruence. These include:
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Non-rigid transformations - These change the size or shape of the figure. For example:
- Scaling (dilation) - Enlarging or reducing the quadrilateral. This change would alter side lengths and angles.
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Shearing - A transformation that distorts the shape but maintains its area.
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Any transformation that alters angle measures or side lengths - This includes non-uniform scaling or more complex geometric transformations.
Therefore, any transformation that does not preserve the properties of congruence (like size and shape) would not result in the two quadrilaterals being congruent.