Hinge Theorem

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

• $m\angle ACB\ >\ m\angle GDE$

• $m\angle ACD\ <\ m\angle GDE$

• $m\angle ACB\ =\ m\angle GDE$

• $\angle ACB\ \cong\ \angle GDE$

Tags

CCSS.7.G.B.5

Compare QT and ST

• $QT\ <\ ST$

• $QT\ >\ ST$

• $QT\ =\ ST$

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

Tags

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

CCSS.HSG.SRT.B.5

Find the range of possible values for x.

• $\frac{7}{2}<x<24$

• $x<6$

• $24<x$

• $\frac{11}{2}<x<6$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Find the range of possible values of x.

• $\frac{5}{3}<x<8$

• $-\frac{3}{2}<x>8$

• $\frac{32}{3}<x<27$

• $27<x<37$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Find the range of possible values for x.

• $2\ <x<6$

• $6<x<15\ \frac{1}{3}$

• $6<x<22$

• $2<x<22$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Find the range of possible values of x.

• $-20<x<21$

• $8<x<37$

• $34<x<37$

• $8<x<24$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Find the range of possible values for x

• $x>7$

• $-\frac{17}{3}<x>7$

• $-\frac{17}{3}<x<7$

• $x<7$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

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

• $m\angle FBG\ <m\angle BFA$

• $m\angle FBG\ >m\angle BFA$

• $m\angle FBG\ \ge m\angle BFA$

• $m\angle FBG\ \le m\angle BFA$

Tags

CCSS.HSG.C.A.2

CCSS.HSG.CO.C.10

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

• $m\angle GBC\ <m\angle FBA$

• $m\angle GBC\ >\ m\angle FBA$

• $m\angle GBC\ \le\ m\angle FBA$

• $m\angle GBC\ \ge\ m\angle FBA$

Tags

CCSS.HSG.CO.C.10