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

The dimensions of one of two triangles that are similar can be obtained

from the other triangle by multiplying by a scale factor.

Reasons:

The given relationship between the triangles are;

Line XY is drawn within ΔRST to form ΔRYX.

XY is parallel to ST

Given that we have;

Point X on side RT and point Y on side RS of ΔRST

ΔRST is similar to ΔRYX, we get;

The ratio of the corresponding sides are equal, which gives;

Therefore;

The option that gives the statement that must be true is;

which is the same as the option; StartFraction RY Over RS EndFraction =

StartFraction RX Over RT EndFraction = StartFraction XY Over TS

EndFraction.

Learn more about the relationship between similar triangles here:

link

link

B. = = , must be true.

Step-by-step explanation:

Similar figures are figures whose angles and sides are similar with respect to a definite ratio when compared.

From the given question, note that ΔRXY is within ΔRST. Given that the two triangles are similar, then their sides can be compare in a form of ratio as:

= =

Therefore by comparing the length of sides of the triangles, option B must be true.

just keep asking questions until you have a better understanding.

step-by-step explanation: