Use the image to answer the question.

Question

An illustration shows two triangles side by side. The two triangles are labeled A B C and D E F. Side A B is congruent to side E F. Side B C is congruent to side F D. Angle B is congruent to angle F, and both measure 70 degrees.

Taima wants to use △ABC
and △EFD
to justify that SAS is a valid triangle congruence criterion. Which of the following is the best first step she could take?

(1 point)
Responses

Translate △ABC
along a vector that takes point A
to point D
.
Translate △ABC
along a vector that takes point cap A to point cap d. - no response given

Translate △ABC
along a vector that takes point C
to point F
.
Translate △ABC
along a vector that takes point cap c to point cap f. - incorrect

Translate △ABC
along a vector that takes point C
to point E
.
Translate △ABC
along a vector that takes point cap c to point cap e. - no response given

Translate △ABC
along a vector that takes point B
to point F
.

Answer 1

To justify that triangles \( \triangle ABC \) and \( \triangle EFD \) are congruent using the SAS (Side-Angle-Side) criterion, Taima should ensure that she aligns the corresponding sides and angles correctly.

Given the information provided:

• \( AB \cong EF \) (these are the first pair of congruent sides)
• \( BC \cong FD \) (these are the second pair of congruent sides)
• \( \angle B \cong \angle F \) (these angles are congruent and are the included angles)

To utilize the SAS criterion, Taima should first align the corresponding angles and sides. The best first step would then be to translate triangle \( \triangle ABC \) such that point \( B \) coincides with point \( F \).

Among the response options, the choice that accomplishes this is:

Translate \( \triangle ABC \) along a vector that takes point B to point F.

This aligns angle \( B \) with angle \( F \) and simultaneously positions side \( AB \) to correspond with side \( EF \). Once this alignment is made, the next step would be to ensure that the remaining sides correspond correctly, which can then justify the use of the SAS criterion.