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Answered

Using side lengths only, could the triangles be similar?

Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.
Yes, StartFraction 0.5 Over 1 EndFraction = StartFraction 0.5 Over 1 EndFraction.
Yes, One-half = StartFraction 0.5 Over 1 EndFraction.
Yes, StartFraction 1.5 Over 1 EndFraction = StartFraction 2 Over 1.5 EndFraction.

Answer :

The triangles are not similar as the ratios are different.

How to depict the triangle?

ΔXYZ

XY = 1.5, XZ = 1, ZY = 2

Δ QSR

QR =1, RS = 1.5, SQ = 0.5

Ratios:

XY/SQ = 1.5/0.5

XZ/QR = 1/1  

ZY/RS = 2/1.5

The answer is no because ratios are different

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