Question

since ( mangle e = 90^{circ}), (\triangle def) is a right triangle and the pythagorean theorem applies. write an equation representing the relationship between the sides of (\triangle def). use ( de), ( df), and ( ef) to represent the lengths of the sides.

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.

Step2: Identify the legs and hypotenuse

In right - triangle \( \triangle DEF\) with \( \angle E = 90^{\circ}\), the legs are \(DE\) and \(EF\), and the hypotenuse is \(DF\).
So, by the Pythagorean theorem, \(DE^{2}+EF^{2}=DF^{2}\)

Answer:

\(DE^{2}+EF^{2}=DF^{2}\)