Larger Angle Theorem and Triangle Inequality

The Triangle Inequality Theorem states the sum of any two sides in a triangle must be greater than the length of the third side.

• False

• True

The Opposite Side Angle Theorem says If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.

• True

• False

Which of the following sets of side lengths could produce a triangle? Select ALL that apply.

• 7 ft., 4 ft, 5 ft

• 3 in, 6 in, 2 in.

• 6 cm, 6 cm, 12 cm

• 9 mm, 9 mm, 9mm

• 4 m, 6 m, 9 m

Will these three sides form a triangle?

• yes

• no

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

• 17 ft

• 0 ft

• 30 ft

• 31 ft

• 32 ft

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

• A) a=2 b=7 c=10

• B) a=5 b=7 c=9

• C) a=6 b=2 c=10

• D) a=9 b=3 c=12

• A) a + b < c

• B) b + c = a

• C) b + c > a

• D) a + c < b

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