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

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. For \(\triangle DEF\) with \(DE = 4\) and \(EF=9\), we have \(DE + EF>DF\), \(DE + DF>EF\), and \(EF + DF>DE\). So \(DE + EF>DF\) (since \(4 + 9>DF\)).

Step2: Determine the range of \(DF\)

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

Step3: Analyze the type of triangle

Since the side - lengths \(DE = 4\) and \(EF = 9\) are different, and we don't know if \(DF\) is equal to either of them, but assuming \(DF
eq4\) and \(DF
eq9\), \(\triangle DEF\) is a scalene triangle (a triangle with no equal side - lengths).

Answer:

DE + EF>DF, 5<DF<13, \(\triangle DEF\) is a scalene triangle