Question

triangles r, s, and t are all scale copies of one another. triangle s is a scaled copy of r using a scale factor of 3. triangle t is a scaled copy of s using a scale factor of 2. match the scale factors with their corresponding triangles. draw a sketch of the triangles on your dry erase board, if needed. from t to s from s to r from r to t from t to r a. $\frac{1}{6}$ b. $\frac{1}{2}$ c. 6 d. $\frac{1}{3}$

Explanation:

Step1: Recall scale - factor concept

If triangle $S$ is a scaled - copy of $R$ with a scale factor of $k_1 = 3$, then if we go from $S$ to $R$, the scale factor $k_{S
ightarrow R}=\frac{1}{3}$ because going in the reverse direction of scaling, we take the reciprocal of the original scale factor.

Step2: Analyze the relationship between $T$ and $S$

Since triangle $T$ is a scaled - copy of $S$ with a scale factor of $k_2 = 2$, then going from $T$ to $S$, the scale factor $k_{T
ightarrow S}=\frac{1}{2}$ (taking the reciprocal).

Step3: Find the scale factor from $R$ to $T$

Since $S$ is a scaled - copy of $R$ with a scale factor of 3 and $T$ is a scaled - copy of $S$ with a scale factor of 2, the scale factor from $R$ to $T$ is $k_{R
ightarrow T}=3\times2 = 6$. Then going from $T$ to $R$, the scale factor $k_{T
ightarrow R}=\frac{1}{6}$.

Answer:

From $T$ to $S$: b. $\frac{1}{2}$
From $S$ to $R$: d. $\frac{1}{3}$
From $R$ to $T$: c. 6
From $T$ to $R$: a. $\frac{1}{6}$