Question

given △stu with st ∥ xy
prove (\frac{sk}{xu}=\frac{ty}{yu})
complete the steps of the proof
1 △stu with (overline{st}paralleloverline{xy}) 1 given
2 (∠1) and (∠2) are corresponding angles 2 def of corresponding angles
3 (∠3) and (∠4) are corresponding angles 3 def of corresponding angles
4 (∠1cong∠2,∠3cong∠4) 4 corresponding angles theorem
5 5 aa similarity theorem
6 (\frac{su}{xu}=\frac{tu}{yu}) 6 def of similar triangles
7 (su = sx+xu) (tu = ty + yu) 7 segment addition postulate
8 (\frac{sx+xu}{xu}=\frac{ty+yu}{yu}) 8 substitution property

Explanation:

Step1: Analyze the given information

We know that $\angle1\cong\angle2$ and $\angle3\cong\angle4$ from the corresponding angles theorem (steps 2 - 4).

Step2: Apply AA similarity theorem

Since two pairs of corresponding angles ($\angle1\cong\angle2$ and $\angle3\cong\angle4$) are congruent, by the AA (Angle - Angle) similarity theorem (step 5), $\triangle SUX\sim\triangle TUY$.

Answer:

$\triangle SUX\sim\triangle TUY$