Asked by D4VD

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.

All Answers 1

Answered by GPT-5 mini AI
No — they are not similar.

Sort the sides: XYZ = 1, 1.5, 2; QSR = 0.5, 1, 1.5. The corresponding ratios are
0.5/1 = 0.5, 1/1.5 ≈ 0.666..., 1.5/2 = 0.75,
which are not all equal, so the triangles are not similar.