Question

problems 2 - 4: here are seven triangles. 2. which triangles are scaled copies of triangle t? 3. 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

|a|
|b|
|c|
|d|
|e|
|f|

Explanation:

Step1: Recall scaled - copy concept

Scaled copies have proportional side - lengths. For triangle \(T\) with side - lengths \(3\), \(4\), \(5\).

Step2: Check triangle \(A\)

The side - lengths of \(A\) are \(4\), \(5\), \(6\). \(\frac{4}{3}
eq\frac{5}{4}
eq\frac{6}{5}\), so \(A\) is not a scaled copy.

Step3: Check triangle \(B\)

The side - lengths of \(B\) are \(3\), \(4\), \(5\), same as \(T\). Scale factor \(k = 1\) since \(\frac{3}{3}=\frac{4}{4}=\frac{5}{5}=1\).

Step4: Check triangle \(C\)

The side - lengths of \(C\) are \(4\), \(5\), \(6.4\). \(\frac{4}{3}
eq\frac{5}{4}
eq\frac{6.4}{5}\), so \(C\) is not a scaled copy.

Step5: Check triangle \(D\)

The side - lengths of \(D\) are \(4.5\), \(6\), \(7.5\). \(\frac{4.5}{3}=\frac{6}{4}=\frac{7.5}{5}=1.5\), so \(D\) is a scaled copy with scale factor \(1.5\).

Step6: Check triangle \(E\)

The side - lengths of \(E\) are \(6\), \(8\), \(10\). \(\frac{6}{3}=\frac{8}{4}=\frac{10}{5}=2\), so \(E\) is a scaled copy with scale factor \(2\).

Step7: Check triangle \(F\)

The side - lengths of \(F\) are \(6\), \(7\), \(8\). \(\frac{6}{3}
eq\frac{7}{4}
eq\frac{8}{5}\), so \(F\) is not a scaled copy.

Answer:

Triangle	Scale Factor
\(B\)	\(1\)
\(C\)
\(D\)	\(1.5\)
\(E\)	\(2\)
\(F\)