Question

1. for each scaled copy, write the scale factor that takes triangle t to that triangle. leave blank if it is not a scaled copy

triangle scale factor

Explanation:

Step1: Define scale - factor formula

The scale factor $k$ from triangle $T$ (assume side - lengths $a,b,c$) to another triangle (side - lengths $a',b',c'$) is given by $k=\frac{a'}{a}=\frac{b'}{b}=\frac{c'}{c}$ if the triangles are similar.

Step2: Check triangle A

Let's assume triangle $T$ has side - lengths $4,5,6$. For triangle $A$ with side - lengths $4,5,6$, the scale factor $k = \frac{4}{4}=\frac{5}{5}=\frac{6}{6}=1$.

Step3: Check triangle B

For triangle $B$ with side - lengths $3,4,5$, if we assume the ratio of corresponding sides: $\frac{3}{4}
eq\frac{4}{5}
eq\frac{5}{6}$, so it is not a scaled copy (leave blank).

Step4: Check triangle C

For triangle $C$ with side - lengths $4,5,6.4$, $\frac{4}{4} = 1$, $\frac{5}{5}=1$, $\frac{6.4}{6}
eq1$, so it is not a scaled copy (leave blank).

Step5: Check triangle D

For triangle $D$ with side - lengths $4.5,6,7.5$. The ratio of side - lengths: $\frac{4.5}{4}=\frac{9}{8}$, $\frac{6}{5}=\frac{6}{5}$, $\frac{7.5}{6}=\frac{5}{4}$. Since $\frac{9}{8}
eq\frac{6}{5}
eq\frac{5}{4}$, it is not a scaled copy (leave blank).

Step6: Check triangle E

For triangle $E$ with side - lengths $6,8,10$. The ratio of side - lengths: $\frac{6}{4}=\frac{3}{2}$, $\frac{8}{5}=\frac{8}{5}$, $\frac{10}{6}=\frac{5}{3}$. Since $\frac{3}{2}
eq\frac{8}{5}
eq\frac{5}{3}$, it is not a scaled copy (leave blank).

Step7: Check triangle F

For triangle $F$ with side - lengths $6,7,8$. The ratio of side - lengths: $\frac{6}{4}=\frac{3}{2}$, $\frac{7}{5}=\frac{7}{5}$, $\frac{8}{6}=\frac{4}{3}$. Since $\frac{3}{2}
eq\frac{7}{5}
eq\frac{4}{3}$, it is not a scaled copy (leave blank).

Answer:

Triangle A: 1
Triangle B:
Triangle C:
Triangle D:
Triangle E:
Triangle F: