Atriangle is rotated 35° about the origin. what is true about the relationship between the image and the pre-image? a.) the lengths of the sides and the measures of the angles are preserved, so the triangles are congruent. b.) the length of the sides are enlarged and measures of the angle are preserved, so the triangles are similar. c.) the lengths of the sides change and the measures of the angles change as well, so the triangle look nothing alike. d.) the lengths of the sides are reduced and measures of the angles are preserved, so one triangle is a reduction of the other.

A.) The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent. It's easier to demonstrate this instead of using math. Take a piece of graph paper and draw an X and Y axis on it. Then take a sheet of clear plastic and place that over the graph paper. Now draw a triangle on that piece of plastic. Now, push a pin through the plastic and through the origin on the graph paper. Finally, rotate the sheet of plastic around the pin to various angles. Does the shape of the drawn triangle ever change, regardless of how much or little you rotate it? The answer is "no". No matter what the rotation, the image and pre-image if the triangle remains congruent.

The rotation of any polygon, or in this case, triangle, does not change the angles and the measure of its sides. Hence, both the lengths of the sides and measures of the angles are preserved. 

Because of the preserved measures of all sides and angles then, the polygon are CONGRUENT. The answer to this item is therefore letter A.