Question

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.

Answer 1

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.