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 and △DEF ratios

$\frac{AC}{DF} = \frac{14}{8} = 1.75$, $\frac{BC}{EF} = \frac{20}{10} = 2$. Ratios not equal.

Step2: Check △DEF and △GHI ratios

$\frac{DF}{HI} = \frac{8}{15} \approx 0.53$, $\frac{EF}{GI} = \frac{10}{12} \approx 0.83$. Ratios not equal.

Step3: Check △GHI and △ABC ratios

$\frac{HI}{AC} = \frac{15}{14} \approx 1.07$, $\frac{GI}{BC} = \frac{12}{20} = 0.6$. Ratios not equal.

Step4: Check △GHI and △JKL ratios

$\frac{HI}{JL} = \frac{15}{7} \approx 2.14$, $\frac{GI}{KL} = \frac{12}{10} = 1.2$. Ratios not equal.

Step5: Check △JKL and △ABC ratios

$\frac{JL}{AC} = \frac{7}{14} = 0.5$, $\frac{KL}{BC} = \frac{10}{20} = 0.5$. Ratios equal; both right triangles.

Answer:

△JKL ~ △ABC