Determine whether the pair of triangles is similar. Justify the answer.
Triangle BAC with sides of 3, 3, 2
Triangle EDF with sides of 12,12,8
also the way I described the triangles, each side corresponds with the side underneath it, if that makes sense. like the 2 and the 8, are both on the Bottom of their respective triangles.
Thank you!
yes, ratio between corresponding sides is 4
To determine whether the pair of triangles BAC and EDF is similar, we need to check if their corresponding sides are proportional and if their corresponding angles are congruent.
First, let's compare the corresponding sides:
- Side BA (3 units) corresponds to side ED (12 units).
- Side AC (3 units) corresponds to side DF (12 units).
- Side BC (2 units) corresponds to side EF (8 units).
To check if the sides are proportional, we can create ratios of corresponding sides and see if they are equal:
BA/ED = 3/12 = 1/4
AC/DF = 3/12 = 1/4
BC/EF = 2/8 = 1/4
Since all the ratios are equal to 1/4, this indicates that the corresponding sides of the two triangles are proportional.
Next, we need to compare the corresponding angles:
- Angle B corresponds to angle E.
- Angle A corresponds to angle D.
- Angle C corresponds to angle F.
To check if the angles are congruent, we compare their measures:
Angle B = Angle E
Angle A = Angle D
Angle C = Angle F
Since the angles have the same measures, this indicates that the corresponding angles of the two triangles are congruent.
Therefore, since the corresponding sides are proportional and the corresponding angles are congruent, we can conclude that the pair of triangles BAC and EDF are similar.
Note: It's important to mention that the order of the corresponding sides and angles matter when determining similarity. In this case, you've correctly described the corresponding sides as being "underneath" each other.