Question

question 1
which of the following statements is always true about rigid transformations?
they change the angles but keep the sides the same.
they preserve both the shape and the size of a figure.
they create a mirror image that is smaller than the original.
they make the figure larger or smaller.
question 2
triangle abc is mapped onto triangle abc using a rotation followed by a reflection. what is true about the two triangles?
they are congruent
they are similar
they are not congruent

Explanation:

• Question 1: Rigid transformations (such as translations, rotations, and reflections) do not change the size or shape of a figure. They preserve the lengths of sides and measures of angles. So, the statement "They preserve both the shape and the size of a figure" is correct.
• Question 2: A rotation followed by a reflection is a rigid transformation. Rigid transformations result in congruent figures. Congruent figures have the same shape and size. Similar figures have the same shape but not necessarily the same size. Since it's a rigid transformation, the triangles are congruent.

Answer:

• Question 1: They preserve both the shape and the size of a figure.
• Question 2: They are congruent.