5-5: Triangle Inequality Theorem

Lesson 5-5:

Triangle Inequality Theorem

Can we make a triangle?

Objectives

• Determine if 3 sides can form a triangle

• Find the range for a third side of a triangle given 2 sides

Triangle naming norms

• We use uppercase letters to indicate the angles (A, B, C).

• We use lowercase letters to indicate the sides (a, b, c).

• Side a is opposite angle A, side b is opposite angle B, side c is opposite angle C.

The two given sides of a triangle are 6 and 9. What could the third side be?

Consider that the 6 and 9 could be the 2 larger sides OR the 6 and 9 could be the 2 smaller sides.

Triangle Inequality Theorem

Multiple Select

Do the following lengths form a triangle

3 inches

4 inches

4 inches

• Yes

• No

Multiple Select

Do the following lengths form a triangle

4 inches

3 inches

8 inches

• Yes

• No

Multiple Select

Do the following lengths form a triangle

10 inches

10 inches

20 inches

• Yes

• No

Multiple Select

Do the following lengths form a triangle

4 inches

5 inches

6 inches

• Yes

• No

Multiple Select

Do the following lengths form a triangle

2 inches

10 inches

13 inches

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle. $$11,7,21$$  

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle. $$9,3,10$$  

• Yes

• No

Multiple Choice

State if the three numbers can be measures of the sides of a triangle. $$11,1,12$$  

• Yes

• No

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side. $$10,7$$  

• $$5<x<16$$  

• $$4<x<14$$  

• $$4<x<17$$  

• $$3<x<17$$  

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side. $$12,12$$  

• $$1<x<24$$  

• $$4<x<24$$  

• $$4<x<23$$  

• $$0<x<24$$  

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side. $$8,12$$  

• $$4<x<16$$  

• $$5<x<20$$  

• $$4<x<17$$  

• $$4<x<20$$  

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side. $$10,6$$  

• $$4<x<16$$  

• $$5<x<15$$  

• $$6<x<15$$  

• $$4<x<14$$  

Multiple Choice

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6?

• 6

• 7

• 5

• 4

Multiple Choice

Which of the following does not represent the lengths of the sides of a triangle?

• 2 cm, 6 cm, 7 cm

• 5 cm, 2 cm, 5 cm

• 5 cm, 5 cm, 8 cm

• 3 cm, 10 cm, 15 cm