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.

Question

orchedork orchedork

27-07-2015
Mathematics

Answered

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.

Verified Answer :

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JaySL JaySL · Answer 1 · 2015-07-27T18:47:57-04:00

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.