Question

quadrilateral abcd is the result of translating quadrilateral abcd by 5 units to the left and 5 units down. select all of the correct statements about the unchanged properties of quadrilateral abcd and quadrilateral abcd. choose all answers that apply. a ∠c and ∠c have the same measures. b the areas of quadrilateral abcd and quadrilateral abcd are the same. c the perimeters of quadrilateral abcd and quadrilateral abcd are the same. d none of the above

Explanation:

Step1: Recall translation properties

Translation is a rigid - motion transformation. Rigid - motion transformations preserve angle measures, side lengths, perimeter, and area.

Step2: Analyze angle measure

Since translation is a rigid - motion, corresponding angles in the pre - image and image have the same measure. So, $\angle C$ and $\angle C'$ have the same measures.

Step3: Analyze area

The area of a figure is preserved under translation because the shape and size of the figure do not change. So, the areas of quadrilateral $ABCD$ and quadrilateral $A'B'C'D'$ are the same.

Step4: Analyze perimeter

The side lengths of a figure are preserved under translation. Since perimeter is the sum of side lengths, the perimeters of quadrilateral $ABCD$ and quadrilateral $A'B'C'D'$ are the same.

Answer:

A. $\angle C$ and $\angle C'$ have the same measures.
B. The areas of quadrilateral $ABCD$ and quadrilateral $A'B'C'D'$ are the same.
C. The perimeters of quadrilateral $ABCD$ and quadrilateral $A'B'C'D'$ are the same.