According to the substitution property of equality [tex]\rm m_{QS} \times m_{US}= -\dfrac{QR}{RS}\times \dfrac{TU}{ST}[/tex] and this can be determined by using the given data.
Given :
- QS is perpendicular to the US.
- Triangle QRS is similar to triangle STU.
The following steps can be used in order to determine the missing statement:
Step 1 - According to the given data, QS is perpendicular to the US and triangle QRS is similar to triangle STU.
Step 2 - According to the similar property of triangles:
[tex]\rm \dfrac{QR}{RS}=\dfrac{ST}{TU}[/tex]
Step 3 - Now, the slope of the line QS is given by:
[tex]\rm m_{QS} = -\dfrac{QR}{RS}[/tex]
Step 4 - The slope of the line US is given by:
[tex]\rm m_{US} = \dfrac{TU}{ST}[/tex]
Step 5 - Now, according to the substitution property of equality:
[tex]\rm m_{QS} \times m_{US}= -\dfrac{QR}{RS}\times \dfrac{TU}{ST}[/tex]
Therefore, the correct option is D).
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https://brainly.com/question/10652623
