Triangle Inequality Theorem

Triangle Inequality Theorem

​Dr. Tom Giles

Multiple Choice

Can the side lengths 7, 8 and 13 form a triangle?

• Yes

• No

Multiple Choice

Can the side lengths 4, 9 and 16 form a triangle?

• Yes

• No

Multiple Choice

Can the side lengths 5, 5 and 10 form a triangle?

• Yes

• No

Multiple Choice

Name the angles from smallest to largest.

• < A, < B, < C

• < A, < C, < B

• < C, < A, < B

• < B, < A, < C

• < C, < B, <A

Multiple Choice

Name the sides from smallest to largest.

• AB, BC , AC

• AB, AC, BC

• BC, AB, AC

• BC, AC, AB

• AC, BC, AB

Multiple Choice

Name the angles from largest to smallest.

• < A, < C, < B

• < A, < B, < C

• < C, < A, < B

• < B, < A, < C

• < B, < C, < A

Multiple Choice

Name the sides from largest to smallest.

• AB, AC, BC

• AB, BC, AC

• AC, AB, BC

• BC, AB, AC

• BC, AC, AB

Multiple Choice

Determine if it is possible to form a triangle with the given side lengths. 7 yd, 8 yd, 9 yd

• yes
• no

Multiple Choice

Determine if it is possible to form a triangle with the given side lengths. 15 in., 12 in., 2 in.

• yes
• no

Multiple Select

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

• 4, 4, 4

• 5, 5, 10

• 3, 6, 9

• 5, 7, 11

• 13, 5, 6

Multiple Choice

Which set of numbers may represent the lengths of the sides of a triangle?

• {2,5,9}
• {6,6,7}
• {6,4,2}           
• {7,8,1}

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

Can the sides of a triangle have lengths 3, 4, and 9?

• Yes

• No

• I don't know

• Cannot be determined

Multiple Choice

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

• I don't know.

• Cannot be determined

Multiple Choice

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
$$12,7$$  

• $$5<x<18$$  

• $$6<x<19$$  

• $$5<x<19$$  

• $$7<x<19$$  

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.
$$12,12$$  

• $$1<x<24$$  

• $$4<x<24$$  

• $$4<x<23$$  

• $$0<x<24$$  

Multiple Choice

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

• $$5<x<16$$  

• $$4<x<14$$  

• $$4<x<17$$  

• $$3<x<17$$  

Multiple Choice

What is the range of values of x for a triangle's third side given side measures of 4 and 12?

• between 8 and 16

• less than 4, greater than 12

• between 4 and 12

Multiple Choice

In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches. Which of the following could be the length of side AC?

• 16 inches

• 5 inches

• 32 inches

• 29 inches

Multiple Choice

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

• more than 3 but less than 11

• more than 11 but less than 3

• less than 3 but more than 11

Multiple Choice

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

• more than 6 but less than 20

• more than 20 but less than 6

• less than 6 but more than 20

Multiple Choice

If the sides of a triangle have the following lengths, find a range of possible values for x.

$$PQ=7x+13,\ QR=10x-2,\ PR=x+27$$  

• $$-3<x<1$$  

• $$1<x<21$$  

• $$-3<x<21$$  

• $$21>x>1$$  

Multiple Choice

If the sides of a triangle have the following lengths, find a range of possible values for x.

$$PQ=6x+3,\ QR=4x-17,\ PR=x+40$$  

• $$-20<x<6$$  

• $$6<x<20$$  

• $$-20<x<20$$  

• $$20>x>6$$  

Multiple Choice

Can these sides form a triangle? 2, 9, 5

• Yes

• No

Multiple Choice

Can these sides form a triangle? 6, 4, 4

• Yes

• No

Multiple Choice

Can these sides form a triangle? 22, 22, 22

• Yes

• No

Multiple Choice

Can these sides form a triangle?

$$6\ \frac{1}{4},\ 14\ \frac{1}{2},\ 6\ \frac{1}{2}$$  

• Yes

• No

Open Ended

Name a possible length for the third side of a triangle with sides 4 and 7.

Open Ended

Name a possible length for the third side of a triangle with sides 11 and 19.

Multiple Select

Which of the following could be the third side of a triangle with sides 5.2 and 7.2? Check all that apply.

• 21

• 2

• 9

• 12.4

• 11

Multiple Select

Which of the following could NOT be the third side of a triangle with sides 35 and 14? Check all that apply.

• 21

• 48

• 26

• 35

• 14

Multiple Choice

If the measures of 2 sides of a triangle are 57 and 32, what is the LEAST possible measure of the third side if the measure is an integer?

• 25

• 26

• 88

• 89

Multiple Choice

What is the LONGEST side in this figure? Be careful...this is tricky!

• AB

• BC

• CD

• DA

• DB

Multiple Choice

List the sides of triangle ABC in ASCENDING order if <A=36 degrees and <B=81 degrees. 

• AB, BC, CA

• BC, AB, AC

• BC, AC, BA