The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].
Given that,
Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].
Triangle RST is shown.
Line XY is drawn parallel to side ST within triangle RST to form a triangle [tex]\rm \triangle RYX[/tex].
We have to determine,
If the triangles are similar, which must be true?
According to the question,
Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].
Triangle RST is shown.
The relationship between the triangles is line XY is drawn parallel to side ST within triangle RST to form [tex]\rm \triangle RYX[/tex].
The point X on side RT and point Y on side RS in [tex]\rm \triangle RYX[/tex].
Then,
The [tex]\rm \triangle RST[/tex] is similar to [tex]\rm \triangle RYX[/tex], the corresponding ratio of their sides are equal,
[tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex]
Hence, The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].
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