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.

The graph isn’t that clear

Ttgffgfdddtdydyfydys