In △QRS, QR = 7, RS = 11, and m∠R = 42. In △UVT, VT = 28, TU = 44 and m∠T = 42. Are the polygons similar? If they are, write a similarity statement and give the similarity ratio

A) QRS = TUV; 11:28

B) QRS = TUV; 7:44

C) The triangles are not similar

D) QRS~VTU; 1:4

Question

Christine Dickerson

Mathematics

6 May, 11:12

In △QRS, QR = 7, RS = 11, and m∠R = 42. In △UVT, VT = 28, TU = 44 and m∠T = 42. Are the polygons similar? If they are, write a similarity statement and give the similarity ratio

A) QRS = TUV; 11:28

B) QRS = TUV; 7:44

C) The triangles are not similar

D) QRS~VTU; 1:4

+5

Answers (1)

Know the Answer?

Berger · Answer 1

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles. Then, we have to check the proportionality of the sides. If these triangles are equal, then VT/QR=UT/RS. If we calculate it, 28/7=44/11=4. This last number is the similarity ratio and since we have proportionality, ΔQRS ~ ΔVTU. The correct answer is D)

In △QRS, QR = 7, RS = 11, and m∠R = 42. In △UVT, VT = 28, TU = 44 and m∠T = 42. Are the polygons similar? If they are, write a similarity statement and give the similarity ratioA) QRS = TUV; 11:28B) QRS = TUV; 7:44C) The triangles are not similarD) QRS~VTU; 1:4

In △QRS, QR = 7, RS = 11, and m∠R = 42. In △UVT, VT = 28, TU = 44 and m∠T = 42. Are the polygons similar? If they are, write a similarity statement and give the similarity ratio

A) QRS = TUV; 11:28

B) QRS = TUV; 7:44

C) The triangles are not similar

D) QRS~VTU; 1:4