Question

1. choose the correct answer(s). which transformations preserve congruence? dilations with a scale factor of 1 dilations when scale factor is greater than 1 or between 0 and 1 translations rotations reflections

Explanation:

To determine which transformations preserve congruence, we analyze each option:

• Reflections: A reflection is a rigid transformation. It flips a figure over a line, but the shape and size (side lengths, angles) remain unchanged. So, reflections preserve congruence.
• Rotations: A rotation is a rigid transformation. It turns a figure around a fixed point, and the side lengths and angles of the figure stay the same. Thus, rotations preserve congruence.
• Translations: A translation is a rigid transformation. It slides a figure from one position to another without changing its shape or size. So, translations preserve congruence.
• Dilations with a scale factor of 1: A dilation with a scale factor of 1 means the figure is not enlarged or reduced. The image is identical to the original figure, so it preserves congruence (essentially an identity transformation in terms of dilation).
• Dilations when the scale factor is greater than 1 or between 0 and 1: Dilations with a scale factor other than 1 change the size of the figure (enlarge or reduce it). Since congruence requires the figures to have the same shape and size, these dilations do not preserve congruence.

Answer:

• Reflections
• Rotations
• Translations
• Dilations with a scale factor of 1