Inequalities in Triangles

Inequalities in Triangles

(Exterior Angle Inequality Theorem & Hinge Theorem)

• Hinge Theorem (SAS Inequality Theorem)

• Converse of Hinge Theorem (SSS Inequality Theorem)

Inequalities in Two Triangles

Inequalities in One Triangle

Inequalities in Triangles

Multiple Choice

Which of ∠2, ∠4, and ∠6 has the largest measure?

• ∠2

• ∠4

• ∠6

Multiple Choice

Which of ∠4, ∠5, and ∠1 has the largest measure?

• ∠4

• ∠5

• ∠1

Multiple Choice

Which of ∠1, ∠7, and ∠2 has the largest measure?

• ∠1

• ∠7

• ∠2

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠7 _____ ∠2

• <

• >

• =

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠6 _____ ∠8

• <

• >

• =

Multiple Choice

Using the figure, choose the correct symbol to be used.

∠4 _____ ∠8

• <

• >

• =

Multiple Choice

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.

Multiple Choice

The Hinge Theorem is also called _______________________.

• SSS Inequality Theorem

• SAS Inequality Theorem

• ASA Inequality Theorem

• SAA Inequality Theorem

Multiple Choice

The Converse of the Hinge Theorem is also called _______________________.

• SSS Inequality Theorem

• SAS Inequality Theorem

• ASA Inequality Theorem

• SAA Inequality Theorem

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

• >

• <

• =

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

• <

• >

• =

Multiple Choice

• <

• >

• =

Multiple Choice

Compare QT and ST

• $$QT\ <\ ST$$

• $$QT\ >\ ST$$

• $$QT\ =\ ST$$

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

Multiple Choice

Complete with >, < or =.

• >

• <

• =

• I don't know.

Multiple Choice

Which inequality relates ∠GBC and ∠FBA ?

• $$m\angle GBC\ <m\angle FBA$$

• $$m\angle GBC\ >\ m\angle FBA$$

• $$m\angle GBC\ \le\ m\angle FBA$$

• $$m\angle GBC\ \ge\ m\angle FBA$$

Multiple Choice

What conclusion can be drawn in the illustration if  $$\overline{SR}>\overline{MJ}$$ ?

• $$\angle x>\angle y$$  

• $$\angle x>\angle z$$  

• $$\angle z>\angle x$$  

• $$\angle z<\angle x$$  

Multiple Choice

• Neva

• Shawn

Multiple Choice

Answer the question that follows.

• Plane 1

• Train 2

• Plane 2

• Train 1

Multiple Choice

• Car A

• Car B

Multiple Choice

• 10.5

• 15

• 21

• 28

Multiple Choice

• AB>AC

• AB<AC

• AB=AC

• No conclusion can be made

Multiple Choice

Four students are doing a scavenger hunt starting at the water fountain. They disagree one the directions and split up. Their paths are shown in the diagram. Which pair is closest to the fountain when they stop?

• Luther and Stephanie

• Mario and Lee

Multiple Choice

• Dave

• Ellen

Multiple Choice

Find the range of possible values of x.

• $$-20<x<21$$

• $$8<x<37$$

• $$34<x<37$$

• $$8<x<24$$

Multiple Choice

Find the range of possible values for x.

• $$\frac{7}{2}<x<24$$

• $$x<6$$

• $$24<x$$

• $$\frac{11}{2}<x<6$$

Multiple Choice

Find the range of possible values for x.

• $$2\ <x<6$$

• $$6<x<15\ \frac{1}{3}$$

• $$6<x<22$$

• $$2<x<22$$

Multiple Choice

Find the range of possible values for x

• $$x>7$$

• $$-\frac{17}{3}<x>7$$

• $$-\frac{17}{3}<x<7$$

• $$x<7$$

Multiple Choice

Find the range of possible values of x.

• $$\frac{5}{3}<x<8$$

• $$-\frac{3}{2}<x>8$$

• $$\frac{32}{3}<x<27$$

• $$27<x<37$$