Respuesta :
Answer:
B. [tex]\frac{RY}{RS}[/tex] = [tex]\frac{RX}{RT}[/tex] = [tex]\frac{XY}{TS}[/tex], 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:
[tex]\frac{RY}{RS}[/tex] = [tex]\frac{RX}{RT}[/tex] = [tex]\frac{XY}{TS}[/tex]
Therefore by comparing the length of sides of the triangles, option B must be true.
The dimensions of one of two triangles that are similar can be obtained
from the other triangle by multiplying by a scale factor.
- The statement that must be true is; [tex]\displaystyle \underline{ \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}}[/tex]
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;
[tex]\displaystyle \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}[/tex]
Therefore;
The option that gives the statement that must be true is; [tex]\displaystyle \underline{\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}}[/tex]
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:
https://brainly.com/question/14445094
https://brainly.com/question/13138042
