Question

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

Explanation:

Step1: Check △ABC ~ △DEF

△ABC has legs 14,20; ratio $\frac{14}{20}=\frac{7}{10}$. △DEF has legs 8,10; ratio $\frac{8}{10}=\frac{4}{5}$. Ratios differ. Not similar.

Step2: Check △DEF ~ △GHI

△DEF legs:8,10 (ratio $\frac{4}{5}$). △GHI legs:15,12 (ratio $\frac{15}{12}=\frac{5}{4}$). Ratios not equal. Not similar.

Step3: Check △GHI ~ △ABC

△GHI legs:15,12 (ratio $\frac{5}{4}$). △ABC legs:14,20 (ratio $\frac{7}{10}$). Ratios differ. Not similar.

Step4: Check △GHI ~ △JKL

△GHI legs:15,12 (ratio $\frac{15}{12}=\frac{5}{4}$). △JKL legs:10,7 (ratio $\frac{10}{7}$). Ratios differ. Not similar.

Step5: Check △JKL ~ △ABC

△JKL legs:10,7 (ratio $\frac{10}{7}$). △ABC legs:20,14 (ratio $\frac{20}{14}=\frac{10}{7}$). Ratios equal. Similar.

Answer:

△JKL ~ △ABC