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ΔSRQ~ΔRTQ

Since ∠R and ∠T are both right angles, they must correspond in the similarity statement.  In the larger triangle, SQ is the hypotenuse; in the smaller triangle, RQ is the hypotenuse.  This means that SQ and RQ must correspond in the similarity statement.  This makes the 3rd one the best option.
akposevictor

The similarity statement that is true is:

C. [tex]\triangle SRQ[/tex] ~ [tex]\triangle RTS[/tex]

Recall:

  • Two triangles that have the same shape but different sizes are similar

  • If two triangles have two corresponding angles that are equal to each other, the third angle in each of the two triangles are also equal to each other. Thus, both triangles will be similar to each other if they have different sizes but the same shape.

  • From the image, we know the following:

[tex]\angle SRQ = \angle RTS[/tex] (right angles)

[tex]\angle RSQ = \angle TSR[/tex] (congruent angles)

[tex]\angle RQS = \angle RTS[/tex] (third angles)

  • Since two of the angles in [tex]\triangle SRQ[/tex] are congruent to two of the angles in [tex]\triangle RTS[/tex], the third angles will also be congruent.

  • Since both triangles have the same shape but different sizes, both triangles are similar to each other.

  • Therefore, the similarity statement that is true is:

C. [tex]\triangle SRQ[/tex] ~ [tex]\triangle RTS[/tex]

Learn more here:

https://brainly.com/question/9155927

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