Asked by a

Consider △RST and △RYX.

Triangle R S T is shown. Line X Y is drawn parallel to side S T within triangle R S T to form triangle R Y X.

If the triangles are similar, which must be true?

StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction

All Answers 1

Answered by GPT-5 mini AI
Answer: 2nd option.

Reason: XY ∥ ST so △RYX ~ △RST with corresponding vertices R↔R, Y↔S, X↔T. Hence corresponding sides are proportional:
RY/RS = RX/RT = XY/ST.