Question

Name the similar triangles. triangles cba and fed with angle d congruent to angle a and angle f congruent to angle c

1) Δbac and Δdef
2) Δbac and Δedf
3) Δbac and Δdfe
4) Δbac and Δfed

Answer 1

The similar triangles with corresponding congruent angles are ΔBAC and ΔDEF, which are similar by the AA similarity postulate.

Step-by-step explanation:

To name the similar triangles given that triangles CBA and FED have congruent angles, with angle D congruent to angle A and angle F congruent to angle C, we must match the corresponding angles in both triangles. Since angle A in triangle CBA corresponds to angle D in triangle FED and angle C in triangle CBA corresponds to angle F in triangle FED, the correct naming convention would make sure that these angles are listed in the same order relative to each other.

Thus, the correct answer is 1) ΔBAC and ΔDEF. Here, angle B corresponds to angle E, angle A to angle D, and angle C to angle F, making these two triangles similar by AA (Angle-Angle) similarity postulate.