Step 1

Given,

The triangle JKA with JA = 18. AK=24 and \(\displaystyle\angle{A}={42}^{{\circ}}\)

The triangle WSY with WS = 12. SY=16 and \(\displaystyle\angle{S}={42}^{{\circ}}\)

We have to find the similarity between the triangles.

Step 2

In \(\displaystyle\triangle{J}{A}{K}\ {\quad\text{and}\quad}\ \triangle{W}{S}{Y}\)

\(\displaystyle{\frac{{{J}{A}}}{{{W}{S}}}}={\frac{{{18}}}{{{12}}}}={\frac{{{3}}}{{{2}}}}\)

\(\displaystyle{\frac{{{A}{k}}}{{{S}{Y}}}}={\frac{{{24}}}{{{16}}}}={\frac{{{3}}}{{{2}}}}\)

\(\displaystyle\angle{A}=\angle{S}={42}^{{\circ}}\)

So,

By SAS(side-angle-side) rule of similarity

\(\displaystyle\triangle{J}{A}{K}\sim\triangle{W}{S}{Y}\)

Given,

The triangle JKA with JA = 18. AK=24 and \(\displaystyle\angle{A}={42}^{{\circ}}\)

The triangle WSY with WS = 12. SY=16 and \(\displaystyle\angle{S}={42}^{{\circ}}\)

We have to find the similarity between the triangles.

Step 2

In \(\displaystyle\triangle{J}{A}{K}\ {\quad\text{and}\quad}\ \triangle{W}{S}{Y}\)

\(\displaystyle{\frac{{{J}{A}}}{{{W}{S}}}}={\frac{{{18}}}{{{12}}}}={\frac{{{3}}}{{{2}}}}\)

\(\displaystyle{\frac{{{A}{k}}}{{{S}{Y}}}}={\frac{{{24}}}{{{16}}}}={\frac{{{3}}}{{{2}}}}\)

\(\displaystyle\angle{A}=\angle{S}={42}^{{\circ}}\)

So,

By SAS(side-angle-side) rule of similarity

\(\displaystyle\triangle{J}{A}{K}\sim\triangle{W}{S}{Y}\)