Triangle Sum Theorem and Triangle Inequality Theorem with Angles

What is the Triangle Inequality Theorem?

• The sum of the angles in a triangle is 180°

• The sum of the lengths of any two sides in a triangle must be greater than the length of the third side

• The longest side of a triangle is opposite the largest angle

• A triangle can have at most one right angle

Which of the following is a property of an equilateral triangle?

• All angles are right angles

• All sides and angles are congruent

• It has one obtuse angle

• It has two acute angles

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°

• 90°

• 180°

• 360°

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

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

Measurements of 15 ft, 15 ft, and ​​ (a)   form a triangle.

• 17 ft

• 0 ft

• 30 ft

• 31 ft

• 32 ft

Solve for the value of x.

• 49

• 58

• 70

• 94

Find the measure of the indicated angle. 

• 26

• 36

• 85

• 144

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