Question

question 1 are the triangles similar? if so, complete the similarity statement and state how you know they are similar. △efg∼______ △nml by sss ∼ △mnl by sss ∼ △lmn by sss ∼ △nlm by sss ∼ not similar

Explanation:

Step1: Calculate side - length ratios

For \(\triangle EFG\) with side - lengths \(EF = 63\), \(FG=28\), \(EG = 56\) and \(\triangle NML\) with side - lengths \(NM = 18\), \(ML = 8\), \(LN = 16\). Calculate the ratios of corresponding sides: \(\frac{EF}{NM}=\frac{63}{18}=\frac{7}{2}\), \(\frac{FG}{ML}=\frac{28}{8}=\frac{7}{2}\), \(\frac{EG}{LN}=\frac{56}{16}=\frac{7}{2}\).

Step2: Apply SSS similarity criterion

Since the ratios of the corresponding sides of \(\triangle EFG\) and \(\triangle NML\) are equal (\(\frac{EF}{NM}=\frac{FG}{ML}=\frac{EG}{LN}=\frac{7}{2}\)), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

\(\triangle EFG\sim\triangle NML\) by SSS