Hinge Theorem and Inequalities in a Triangle

It is called the HINGE theorem, because...

• the vertex of the angle acts like a hinge to open the triangle.

• it's named after Joseph Hinge, the man who discovered it.

• "hinge" is the Spanish word for angle.

• the triangle makes a hinge shape, like a tent.

Compare $m\angle ACD\ and\ m\angle GDE$

Compare QT and ST

Find the range of possible values for x.

Find the range of possible values of x.

Find the range of possible values for x.

Find the range of possible values of x.

Find the range of possible values for x

Which inequality relates $\angle FBG\ and\ \angle BFA$ ?

Which inequality relates $\angle GBC\ and\ \angle FBA$ ?