Side Lengths of Triangles

6.8A Side Lengths of Triangles

​Part 1: Side Lengths and Angles in Triangles

Part 2: Triangle Inequality Theorem

Angles and Sides

• The smallest angle will be opposite the  shortest side

• While the largest angle will be opposite the longest side.

• A side is congruent to another side if it has an equal length.

Use Inequalities in Triangles

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which side of the triangle should be the longest?

• A

• B

• C

Multiple Choice

What is the smallest angle?

• K
• L
• M

Multiple Choice

What is the biggest side?

• LM
• MN
• LN

Triangle Inequality

To form a triangle, the sum of any two side lengths MUST be GREATER THAN the last side length.

a + b > c

b + c > a

a + c > b

Triangle Inequality

Not every group of three segments can be used to form a triangle. The lengths of the segments must fit a certain relationship.

Multiple Choice

Will these side lengths form a triangle?

12, 2, 18

• yes

• no

Multiple Choice

Will these three sides form a triangle?

26, 5, 24

• yes

• no

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60

• 28, 30, 58

• 13, 20, 27

• 2, 4, 5

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 side lengths could NOT be used to form a triangle?

• 2 cm, 6 cm, 7 cm

• 7 cm, 15 cm, 8 cm

• 5 cm, 5 cm, 5 cm

• 8 cm, 9 cm, 6 cm

Multiple Choice

Two sides of a triangle have measures of 6 inches and 12 inches. Which measure could be the length of the third side?

Hint:

• 5 in

• 6 in

• 10 in

• 18 in

Multiple Choice

What is the smallest side?

• EF
• FG
• EG

Multiple Choice

What is the biggest side? (Hint: its across from the biggest angle)

• EF
• FG
• EG

Multiple Choice

Which side of the triangle should be the longest?

• A

• B

• C

Multiple Choice

What is the smallest side?

• LM

• MN

• LN