Angle Sum Triangle Inequality Theorems

Two sides of a triangle have side lengths of 17 meters and 12 meters.  What is the range of possible lengths for the third side?

• 12 < x < 17

• 12 < x < 29

• 5 < x < 17

• 5 < x < 29

The Triangle Inequality Theorem states the sum of the lengths of any two sides of a triangle is ________________ the length of the third side.

• greater than

• less than

• equal to

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

• 32, 34, 60

• 28, 30, 58

• 13, 20, 27

• 2, 4, 5

Which two angles are the remote interior angles to Angle W?

• Angle X and Angle Y

• Angle X and Angle Z

• Angle Y and Angle Z

• Angle Z and Angle W

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

• 4 < x < 16

• 6 < x < 16

• 5 < x < 16

• 4 < x < 15

Max cut strips of plywood for a home improvement project. Two of the strips were 8 inches each and the third strip was 14 inches. Could Max make a triangle with these strips of plywood?​ (a)   because the sum of the 2 shorter sides is ​ (b)   the longest side.

• Yes

• greater than

• No

• less than

Which equation can be used to find the value of x?

• 11x + 25x = 90

• 11x + 25x + 9x = 90

• 11x + 25x = 180

• 11x + 25x + 9x = 180

Noah cut strips of plywood for a home improvement project. Two of the strips were 14 inches each and the third strip was 30 inches. Could Noah make a triangle with these strips of plywood?

​ ​ (a)   because the sum of the 2 shorter sides is ​ ​ (b)   the longest side.

• No

• less than

• Yes

• greater than

7. State if the three numbers can be the measures of the sides of a triangle.

• A. Yes

• B. No

Will these side lengths form a triangle?

• yes

• no