Hinge Theorem and Inequalities in a Triangle

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$$\angle A$$  

$$\angle B$$  

$$\angle C$$  

$$\angle D$$  

$$\angle1$$  

$$\angle2$$  

$$\angle A$$  

$$\angle B$$  

$$\angle C$$  

$$\angle D$$  

Less than

Greater than

Equal to 

Half of

$$m\angle ACB\ >\ m\angle GDE$$

$$m\angle ACD\ <\ m\angle GDE$$

$$m\angle ACB\ =\ m\angle GDE$$

$$\angle ACB\ \cong\ \angle GDE$$

$$QT\ <\ ST$$

$$QT\ >\ ST$$

$$QT\ =\ ST$$

$$\overline{QT}\ \cong\ \overline{ST}$$

$$2\ <x<6$$

$$6<x<15\ \frac{1}{3}$$

$$6<x<22$$

$$2<x<22$$

$$-20<x<21$$

$$8<x<37$$

$$34<x<37$$

$$8<x<24$$

$$m\angle FBG\ <m\angle BFA$$

$$m\angle FBG\ >m\angle BFA$$

$$m\angle FBG\ \ge m\angle BFA$$

$$m\angle FBG\ \le m\angle BFA$$

$$m\angle GBC\ <m\angle FBA$$

$$m\angle GBC\ >\ m\angle FBA$$

$$m\angle GBC\ \le\ m\angle FBA$$

$$m\angle GBC\ \ge\ m\angle FBA$$

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