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.

Question

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 C
to point E
.
Translate triangle upper A upper B upper C along a vector that takes point upper C to point upper E .

Translate △ABC
along a vector that takes point B
to point F
.
Translate triangle upper A upper B upper C along a vector that takes point upper B to point upper F .

Translate △ABC
along a vector that takes point C
to point F
.
Translate triangle upper A upper B upper C along a vector that takes point upper C to point upper F .

Translate △ABC
along a vector that takes point A
to point D
.

Answer 1

To justify that ΔABC and ΔEFD are congruent using the SAS (Side-Angle-Side) triangle congruence criterion, it is important to correctly position the triangles relative to each other while keeping the corresponding elements in line with the SAS requirement.

In this case, the best first step Taima could take is to translate ΔABC along a vector that takes point B to point F. This step correctly aligns the corresponding sides and the included angle.

Translating ΔABC such that point B moves to point F will position the triangles in such a way that:

• The congruent sides AB and EF are aligned,
• The angle B, which is congruent to angle F, remains as the included angle between the two corresponding sides.

Thus, the correct response is:

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