Question

1. to complete the proof of the hinge theorem, show that assuming ( mangle fde < mangle vtu ) leads to a contradiction of the given statement, ( ef > uv ).

Explanation:

Step1: State the Hinge Theorem

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 is longer than the third side of the second.

Step2: Assume \(m\angle FDE

By the Hinge Theorem, if \(DE = TU\), \(DF=TV\), and \(m\angle FDE

Step3: Contradict the given

But we are given that \(EF>UV\). So the assumption \(m\angle FDE < m\angle VTU\) is wrong.

Answer:

Assuming \(m\angle FDEUV\). So the assumption is false.