One triangle has vertices A, B, and C. Another has vertices T, R, and I. Are the two triangles similar? If so state the similarity and the scale factor.

AB- 6
BC- 8
AC- 10

TR- 10
RI- 7.5
TI- 12.5

arrange in increasing size order to test corresponding sides

RI = 7.5
TR = 10
TI = 12.5

now if all sides are related by the same scale factor, they are similar
7.5/6 = 1.25
10/8 = 1.25
12.5/10 = 1.25
YES!! the corresponding sides are in the same ratio. They are similar with scale factor 1.25

To determine if two triangles are similar, we need to compare the ratios of their corresponding sides. In this case, let's compare the ratios of the corresponding sides of triangle ABC (with sides AB, BC, and AC) to triangle TRI (with sides TR, RI, and TI).

First, let's calculate the ratios of the corresponding sides:

Ratio of AB to TR: AB / TR = 6 / 10 = 0.6
Ratio of BC to RI: BC / RI = 8 / 7.5 = 1.0667
Ratio of AC to TI: AC / TI = 10 / 12.5 = 0.8

Now, let's compare the ratios:

Ratio of AB to TR is different from the ratio of BC to RI, indicating that the triangles are not similar.

Therefore, the two triangles are not similar, and we cannot determine a scale factor.