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23 June, 02:28

Given the information below, is triangle QRS similar to triangle UVT? If so, give the scale factor.

QR = 8, RS = 16, UV = 18, VT = 34, Angle S = 36 degrees, and Angle T = 36 degrees.

A.

No, the triangles are not similar.

B.

Yes, the scale factor is 1:2.

C.

Yes, the scale factor is 4:9.

D.

Yes, the scale factor is 8:17.

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Answers (1)
  1. 23 June, 05:12
    0
    The triangles are not similar. QR/RS is 8/16=1/2, but UV/VT is 18/34=9/17. As these are not equal, the triangles are not similar.

    Notice that if VT was equal to 36, then UV/VT would be 18/36=1/2 as well, but because S is not between QR and RS, and T is not between UV and VT, the triangles would still not be similar, because to use SAS similarity, the similar angle must be between the two similar sides.
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