Use the image to answer the question.

Question

the image shows two triangles. Triangle #1 ABC has a degree of 70 degrees. Triangle #2 DEF has a degree of 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) Translate △ABC
along a vector that takes point C
to point E
.2) Translate △ABC
along a vector that takes point A
to point D
.3) Translate △ABC
along a vector that takes point B
to point F
.4) Translate △ABC
along a vector that takes point C
to point F
.

Answer 1

To justify that SAS (Side-Angle-Side) is a valid triangle congruence criterion using triangles ABC and DEF, Taima should focus on ensuring that a side and the angle between that side and another side are the same in both triangles.

Given that both triangles have an angle of 70 degrees and she wants to translate triangle ABC to align with triangle DEF, the best first step would be:

1) Translate △ABC along a vector that takes point C to point E.

This option translates one of the vertices (C) from triangle ABC to match a corresponding vertex (E) in triangle DEF, which can then help in aligning the other sides accordingly to demonstrate the SAS congruence criterion. After this translation, Taima can further manipulate the triangles to verify that the appropriate sides and angle are congruent.