Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is always _________.

• half of the length of the third side

• equal to the length of the third side

• less than the length of the third side

• greater than the length of the third side

The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side. What theorem of triangle inequality is this?

• Angle-Side Relationship Theorem

• Triangle Inequality Theorem

• Exterior Angle Inequality Theorem

• SSS Triangle Inequality Theorem

Which of the following could NOT be used as the length of the sides of a

triangle?

• 4, 4, 4

• 11, 12, 13

• 8, 14, 10

• 6, 5, 12

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

• I don't know

• Secret

In ∆ABC, AB= 3 cm and BC= 4 cm, find the range of the possible length of AC.

• 1 < AC < 7

• 7 < AC < 1

• 7 ≤ AC ≤ 1

• 1 ≤ AC ≤ 7

In ∆ XYZ, XY= 5 cm and YZ= 5 cm, find the range of the possible length of XZ.

• 0 ≤ XZ ≤ 10

• 0 < XZ < 10

• 10 ≤ XZ ≤ 0

• 10 < XZ < 0