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ioda
3 years ago
5

Please help, using Brainly and i can’t figure out this question. Given : A STU with overline ST || XY Prove: (SX)/(XU) = (TY)/(Y

U)

Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

Answer:

The correct answer is;

ΔUXY ≅ Δ UST

Step-by-step explanation:

The given steps are;

1. ΔSTU with \overline{ST}\left |  \right |\overline{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. ∠1 ≅ ∠2; ∠3 ≅ ∠4,                                   4. Corresponding angles theorem

5. ΔUXY ≅ΔUST,                                           5, AA similarity theorem

6. \dfrac{SU}{XU} = \dfrac{TU}{YU},                                               6. Def of similar triangles  

7. SU = SX + XU,                                          7. Segment addition postulate

   TU = TY +  YU,        

8. \dfrac{SX + XU}{XU} = \dfrac{TY + YU}{YU},                           8. Substitution property    

9.  \dfrac{SX }{XU} + 1= \dfrac{TY }{YU}+ 1,                                   8. Algebra simplification        

By subtracting 1 from both sides of the equation, we get;

\dfrac{SX }{XU} = \dfrac{TY }{YU}          

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