Answer:
E, Yes. ∆HJK ~ ∆STV. The scale factor is ½.
Step-by-step explanation:
1. Similarity statement
When you name similar triangles, the order of the letters of corresponding angles must be in matching order.
For example, in ∆HJK, ∠H is the right angle, ∠J is the larger acute angle, and ∠K is the smallest angle.
The corresponding parts in ∆STV are ∠S, ∠T, and ∠V.
The similarity statement is
∆HJK ~ ∆STV
2. Scale factor
The scale factor (C) is the ratio of corresponding parts of the two triangles.
If ∆HJK is transformed to ∆STV, the scale factor is
[tex]C = \dfrac{\text{ST}}{\text{HJ}} = \dfrac{\text{TV}}{\text{JK}} = \dfrac{\text{SV}}{\text{HK}}\\\\C = \dfrac{5}{10} = \dfrac{13}{26} = \dfrac{12}{24} = \mathbf{\dfrac{1}{2}}\\\\\text{The scale factor is $\large \boxed{\mathbf{\dfrac{1}{2}}}$}[/tex]
