Question

problem 15: lesson 45) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: △def prove: ef + fd > de

Explanation:

Step1: Recall triangle - related concepts

In a triangle, the sum of the lengths of any two sides is greater than the length of the third side. This is a fundamental property of triangles.
For \(\triangle DEF\), the sides are \(EF\), \(FD\), and \(DE\).

Step2: Apply the property

According to the triangle - side - length relationship (triangle inequality theorem), for a triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\).
In \(\triangle DEF\), if we let \(a = EF\), \(b=FD\), and \(c = DE\), then by the triangle inequality theorem, \(EF + FD>DE\).

Answer:

Triangle Inequality Theorem.