Question

△RST ~ △RYX by the SSS similarity theorem.


Which ratio is also equal to RT/RX and RS/RY?

XY/TS

SY/RY

RX/XT

ST/YX



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Answer 1

Answer: The correct option is fourth, i.e., $\frac{ST}{YX}$.

Explanation:

It is given that,

$\triangle RST \sim \triangle RYX$

By the rule of of congruence SSS.

Since both triangles are congruent, it means the ratio of their corresponding sides are equal.

The sides of first triangle are RS, ST, RT and their corresponding sides are RY, YX and RX respectively.

So,

$\frac{RS}{RY} =\frac{ST}{YX} =\frac{RT}{RX} =k$

Where, k is any constant.

Since it is given that,

$\frac{RS}{RY}=\frac{RT}{RX}$

and we know that $\frac{ST}{YX}$ is also equal to these ratios, therefore, the fourth option is correct.