Question

1. 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	1.5
e	2

|f|

Explanation:

Step1: Recall scaled - copy concept

Two triangles are scaled copies if the ratios of their corresponding side - lengths are equal. For triangle \(T\) with side - lengths \(3\), \(4\), and \(5\).

Step2: Check triangle A

For triangle \(A\) with side - lengths \(4\), \(5\), and \(6\). Calculate the ratios of corresponding sides: \(\frac{4}{3}
eq\frac{5}{4}
eq\frac{6}{5}\), so \(A\) is not a scaled copy.

Step3: Check triangle B

For triangle \(B\) with side - lengths \(3\), \(4\), and \(5\). The ratios of corresponding sides are \(\frac{3}{3} = 1\), \(\frac{4}{4}=1\), \(\frac{5}{5}=1\). So \(B\) is a scaled copy with scale factor \(1\).

Step4: Check triangle C

For triangle \(C\) with side - lengths \(4\), \(5\), and \(6.4\). \(\frac{4}{3}
eq\frac{5}{4}
eq\frac{6.4}{5}\), so \(C\) is not a scaled copy.

Step5: Check triangle D

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

Step6: Check triangle E

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

Step7: Check triangle F

For triangle \(F\) with side - lengths \(6\), \(7\), and \(8\). \(\frac{6}{3}
eq\frac{7}{4}
eq\frac{8}{5}\), so \(F\) is not a scaled copy.

Answer:

1. Triangles \(B\), \(D\), and \(E\) are scaled copies of triangle \(T\).

3.

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