Answer:
yes, ∆RST ~ ∆XYZ
Step-by-step explanation:
You want to know if ∆RST is similar to ∆XYZ when RS=6, ST=14, XY=9, YZ=21 and ∠S≅∠Y.
SAS similarity
Two triangles are similar by the SAS theorem if corresponding sides have the same ratio, and the angles between them are congruent.
Application
Corresponding sides are ...
RS : XY = 6 : 9 = 2 : 3
ST : YZ = 14 : 21 = 2 : 3 . . . . same ratio
The angles between them are ...
∠S, ∠Y . . . . . given as congruent
Corresponding sides have the same ratios, and the angles between them are congruent, so the triangles are similar.
