Question

based only on the information given in the diagram, it is guaranteed that △jkl ~ △wxy.
a. true
b. false

Explanation:

Step1: Find angles in triangles

In $\triangle JKL$, $\angle J = 27^{\circ}$ and $\angle K=90^{\circ}$, so $\angle L=180^{\circ}-(90^{\circ} + 27^{\circ})=63^{\circ}$. In $\triangle WXY$, $\angle X = 90^{\circ}$ and $\angle Y=63^{\circ}$, so $\angle W=180^{\circ}-(90^{\circ}+63^{\circ}) = 27^{\circ}$.

Step2: Apply AA (Angle - Angle) similarity criterion

Since $\angle J=\angle W = 27^{\circ}$ and $\angle K=\angle X = 90^{\circ}$ and $\angle L=\angle Y = 63^{\circ}$, by the AA similarity criterion for triangles, $\triangle JKL\sim\triangle WXY$.

Answer:

A. True