Question

to write an indirect proof of the hinge theorem, you are given ( overline{ab} cong overline{de}, overline{bc} cong overline{ef} ), and ( mangle b>mangle e ). you must prove that choose > choose. first, you assume that choose. choose... ( mangle b>mangle e ) ( mangle bleq mangle e ) ( ac > df ) ( acleq df )

Explanation:

Step1: Recall the Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. Here, we are given \( \overline{AB}\cong\overline{DE}\), \( \overline{BC}\cong\overline{EF}\), and \(m\angle B > m\angle E\). So we need to prove \(AC>DF\).

Step2: Recall the steps of an indirect proof

In an indirect proof (proof by contradiction), we first assume the opposite of what we want to prove. Since we want to prove \(AC > DF\), the opposite (negation) of \(AC>DF\) is \(AC\leq DF\) (which includes \(AC = DF\) and \(AC

Answer:

You must prove that \(AC>DF\). First, you assume that \(AC\leq DF\).