Question

which statements about the diagram are true? select three options. de + ef > df △def is an isosceles triangle. 5 < df < 13 de + df < ef △def is a scalene triangle.

Explanation:

Step1: Apply triangle inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. For \(\triangle DEF\), \(DE + EF>DF\) (since \(DE = 4\), \(EF\) is not equal to \(4\) but still the sum of two sides \(DE\) and \(EF\) must be greater than \(DF\)).

Step2: Analyze side - length relationships for range of \(DF\)

By the triangle inequality theorem: \(|DE - EF|

Step3: Classify the triangle

Since \(DE = 4\), \(EF = 9\), and \(DF\) is a different length (because \(5eq4\) and \(DF
eq9\)), \(\triangle DEF\) has all three sides of different lengths. A triangle with all sides of different lengths is a scalene triangle.

Answer:

\(DE + EF>DF\), \(5