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

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CCSS.HSG.CO.B.7

Compare QT and ST

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CCSS.HSG.CO.C.9

Find the range of possible values for x.

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CCSS.HSG.CO.C.11

Find the range of possible values of x.

Find the range of possible values for x.

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CCSS.HSG.SRT.A.2

Find the range of possible values of x.

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CCSS.8.G.A.5

Find the range of possible values for x

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

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CCSS.8.G.A.5

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

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CCSS.HSG.CO.C.10