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TConsider △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

Answer :

For similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.

Given that, for ΔRST, line XY is drawn parallel to side ST within ΔRST to form ΔRYX.

Considering ΔRST and ΔRYX.

What is the relation between sides of similar triangles?

The corresponding sides of similar triangles are proportional.

We get ∠RXY=∠RST (Corresponding angles, since XY║ST)

∠RYX=∠RTS (Corresponding angles, since XY║ST)

From AA similarity criteria ΔRST is similar to ΔRYX.

Now, RY/RS = RX/RT = XY/TS.

Therefore, for similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.

To learn more about similar triangles visit:

https://brainly.com/question/25882965.

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