Answer: Triangle ABCD is a parallelogram because it has both pairs of opposite sides parallel. This is because a 180° rotation around the midpoint of segment AC preserves the lengths of the sides of triangle ABC, meaning that the corresponding sides of triangle CDA are congruent to the corresponding sides of triangle ABC. Since opposite sides of a parallelogram are congruent and parallel, triangle ABCD is a parallelogram. Similarly, triangle ABEC is also a parallelogram because a 180° rotation around the midpoint of segment BC preserves the lengths of the sides of triangle ABC, making the corresponding sides of triangle ECB congruent to the corresponding sides of triangle ABC. Therefore, triangle ABEC also has both pairs of opposite sides parallel and is a parallelogram. b. Two pairs of congruent angles in the figure are angle ABD and angle DCA, and angle CBE and angle ECA. These angles are congruent because a 180° rotation around a point preserves angles. When triangle ABC is rotated 180° around the midpoint of segment AC, angle ABD is mapped to angle DCA, and when triangle ABC is rotated 180° around the midpoint of segment BC, angle CBE is mapped to angle ECA. Since the rotations preserve angles, these pairs of angles are congruent.
Step-by-step explanation: My explanation is in the answer