Question

Observe parallelogram ABCD plotted on the coordinate plane below. Part I: Provide the coordinates of a parallelogram A’B’C’D’ that is congruent to parallelogram ABCD. Explain why these figures are congruent. (4 points) Part II: Provide the coordinates of a parallelogram A’’B’’C’’D’’ that is similar to parallelogram ABCD. Explain why these figures are similar. (6 points)

Answer 1

You are given a parallelogram ABCD with the following Cartesian plane coordinates:A:(−7,3)B:(−5,7)C:(1,7)D:(−1,3)and are asked to provide a parallelogram A′B′C′D′ that is congruent to it. The easiest way to do this is to perform a simple shift (either upward or downward) of your original figure. Let us perform a downward shift of 1 unit on it for simplicity:A′:(−7,2)B′:(−5,6)C′:(1,6)D′:(−1,2)Parallelogram A′B′C′D′ is congruent to parallelogram ABCD because their corresponding sides and angles are equal.