If a series of rigid transformations maps ∠F onto ∠C where ∠F is congruent to ∠C, then which of the following statements is true?

triangles ABC and FDE, in which angles A and D are right angles

ΔABC ~ ΔFDE because of the definition of similarity in terms of similarity transformations
ΔABC ~ ΔFDE because of the AA similarity postulate
segment BC ~ segment EF because of the definition of similarity in terms of similarity transformations
segment BC ~ segment EF because corresponding parts of similar triangles are proportional

Rigid transformations is a process which can be used to either enlarge, reduce, resize a given object. Examples are: translation, reflection, rotation etc.

Given that ∠F is congruent to ∠C in the question, this implies that ΔABC is similar to ΔFDE. Thus a scale is required to map the two triangles exactly into one another. Therefore, the statement that is true is segment BC ~ segment EF because corresponding parts of similar triangles are proportional.

aksnkj aksnkj · Answer 2 · 2021-11-18T14:39:55+01:00

It can be concluded that "segment BC ~ segment EF because corresponding parts of similar triangles are proportional ". option D is correct.

Given information:

Triangles ABC and FDE, in which angles A and D are right angles.

∠F is congruent to ∠C.

From the given information, in triangles ABC and FDE,

[tex]\angle A=\angle D=90^{\circ}\\\angle F=\angle C[/tex]

So, by Angle-angle (AA) similarity rule, the two triangles will be similar.

So, [tex]\Delta ABC \sim \Delta DFE[/tex]

Now, the triangles are similar. So, the ratio of their sides will be in the same ratio. It can be written as,

[tex]\dfrac{AB}{DF}=\dfrac{BC}{FE}=\dfrac{AC}{DE}[/tex]

Therefore, it can be concluded that "segment BC ~ segment EF because corresponding parts of similar triangles are proportional ".

For more details, refer to the link:

https://brainly.com/question/19738610