Question

If the triangles are similar, which must be true?

-

RY

YS

RX _ XY

XT TS

1

RY

RS

RX

RT

XY

TS

2 회

RY

RS

III

RX

RT

RS

RY

RY

RX

RS

RT

=

TS

Answer 1

Answer:

B. RY/RS=RX/RT=XY/TS

Step-by-step explanation:

In the picture attached, △RST and △RYX (which are similar) are shown

The options are:

• A. RY/YS=RX/XT=XY/TS

• B.RY/RS=RX/RT=XY/TS

• C.RY/RS=RX/RT=RS/RY

• D.RY/RX=RS/RT=XY/TS

Given that the triangles are similar, then their sides are proportional. Then, there is some constant k, which satisfies:

k*RS = RY

k*RT = RX

k*TS = XY

This can be rewritten as:

k = RY/RS = RX/RT = XY/TS

Answer 2

Since △RST and △RYX are similar triangles, the statement that must be true is:

B. RY/RS = RX/RT = XY/TS

Sides of Similar Triangles

• If two triangles are similar to each other, then, the ratio of their corresponding side lengths must be equal to each other.

Thus, △RST and △RYX  are similar triangles.

• Therefore:

RY/RS = RX/RT = XY/TS

Therefore, since △RST and △RYX are similar triangles, the statement that must be true is:

B. RY/RS = RX/RT = XY/TS

Learn more about similar triangles on:

https://brainly.com/question/14285697