triangle ABC undergoes a series of transformations to result in Triangle DF is triangle DEF congruent to triangle ABC

Answer :Triangle ABC is translated 3 units up and 5 units right , and then rotated 90° clockwise to form traingle DEF.Since, translation and rotation both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.Thus, here ΔABC is congruent to ΔDEF.Triangle ABC is reflected over x axis ,and then translated 6 units down to form triangle DEF.Since, translation and reflection both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.Thus, here ΔABC is congruent to ΔDEF.Triangle ABC is rotated 180°, and then dilated by a scale factor of 3 to form triangle DEF.Here rotation is a rigid transformation which maps only congruent images but dilation is not a rigid transformation because it produces similar images for scale factor other than 1 (with scale factor 1 it also produce congruent images) . Thus, here ΔABC is not congruent to ΔDEF.