consider \\( \\triangle rst \\) and \\( \\triangle ryx \\).\nif the triangles are similar, which must be…

consider \\( \\triangle rst \\) and \\( \\triangle ryx \\).\nif the triangles are similar, which must be true?\n\\( \\frac { r y } { y s } = \\frac { r x } { x t } = \\frac { x y } { t s } \\)\n\\( \\frac { r y } { r s } = \\frac { r x } { r t } = \\frac { x y } { t s } \\)\n\\( \\frac { r y } { r s } = \\frac { r x } { r t } = \\frac { r s } { r y } \\)\n\\( \\frac { r y } { r x } = \\frac { r s } { r t } = \\frac { x y } { t s } \\)

consider \\( \\triangle rst \\) and \\( \\triangle ryx \\).\nif the triangles are similar, which must be true?\n\\( \\frac { r y } { y s } = \\frac { r x } { x t } = \\frac { x y } { t s } \\)\n\\( \\frac { r y } { r s } = \\frac { r x } { r t } = \\frac { x y } { t s } \\)\n\\( \\frac { r y } { r s } = \\frac { r x } { r t } = \\frac { r s } { r y } \\)\n\\( \\frac { r y } { r x } = \\frac { r s } { r t } = \\frac { x y } { t s } \\)

Answer

Explanation:

Step1: Recall the property of similar triangles

If two triangles (\triangle RST) and (\triangle RYX) are similar, then the ratios of their corresponding sides are equal.

Step2: Identify the corresponding sides

In (\triangle RST) and (\triangle RYX), (RY) corresponds to (RS), (RX) corresponds to (RT), and (XY) corresponds to (TS). So, (\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS})

Answer:

(\frac{RY}{RS}=\frac{RX}{RT}=\frac{XY}{TS}) (the second option)