Question

which pairs of triangles are similar? check all that apply. △abc ~ △def △def ~ △ghi △ghi ~ △abc △ghi ~ △jkl △jkl ~ △abc

Explanation:

Step1: Calculate the ratios of sides for each pair

For \(\triangle ABC\) and \(\triangle DEF\): \(\frac{14}{8}=\frac{7}{4}\), \(\frac{20}{10} = 2\). Since \(\frac{7}{4}
eq2\), \(\triangle ABC\) and \(\triangle DEF\) are not similar.

Step2: Calculate ratios for \(\triangle DEF\) and \(\triangle GHI\)

\(\frac{8}{15}
eq\frac{10}{12}\), so \(\triangle DEF\) and \(\triangle GHI\) are not similar.

Step3: Calculate ratios for \(\triangle GHI\) and \(\triangle ABC\)

\(\frac{14}{12}=\frac{7}{6}\), \(\frac{20}{15}=\frac{4}{3}\). Not equal, so not similar.

Step4: Calculate ratios for \(\triangle GHI\) and \(\triangle JKL\)

\(\frac{15}{10}=\frac{3}{2}\), \(\frac{12}{7}
eq\frac{3}{2}\). Not similar.

Step5: Calculate ratios for \(\triangle JKL\) and \(\triangle ABC\)

\(\frac{14}{7}=2\), \(\frac{20}{10}=2\). Since the right - angle is common (AA similarity: right - angle and ratio of sides), \(\triangle JKL\sim\triangle ABC\)

Answer:

\(\triangle JKL\sim\triangle ABC\)