Question

select the statement below that best identifies the relationship between the triangles and the reason why. similar by sss. all corresponding sides are proportional. congruent by sss. all corresponding sides are congruent. similar by sas. two pairs of corresponding sides are proportional and one pair of angles are congruent. neither similar nor congruent. corresponding sides are not proportional or congruent.

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(DEF\) with sides \(4\), \(2\), \(5\) and triangle \(ABN\) with sides \(12\), \(8\), \(15\).

• Ratio of first pair: \(\frac{4}{12}=\frac{1}{3}\)
• Ratio of second pair: \(\frac{2}{8}=\frac{1}{4}\)
• Ratio of third pair: \(\frac{5}{15}=\frac{1}{3}\)

Since \(\frac{1}{3}
eq\frac{1}{4}\), the sides are not proportional. Also, there is no information about angles to use \(SAS\) similarity. And clearly the sides are not congruent (e.g., \(4
eq12\), \(2
eq8\), \(5
eq15\))

Answer:

Neither similar nor congruent. Corresponding sides are not proportional or congruent.