Triangle inequality

Fill in the blanks: According to the triangle inequality theorem, any side of a triangle must be _____ ____ the other two sides of the triangle combined.

• Shorter than

• longer than

• equal

• None of these are correct

Can we form a triangle with line segments that have lengths 2, 8, and 14 units?

• No, because these line segments wouldn't satisfy the triangle inequality theorem.

• Yes, because these line segments satisfy the triangle inequality theorem.

• No, because there are only two sides to a triangle.

• Yes, because 8 < 14.

The measure of an exterior angle of a triangle is always

• greater than its adjacent interior angle.

• less than its adjacent interior angle.

• greater than either remote interior angle.

• less than either remote interior angle.

Each of Xylie, Marie, Angel and Chloe was given an 18-inch piece of stick. They were instructed to create a triangle. Each cut the stick in their own chosen lengths as follows: Xylie—6 in, 6 in, 6 in; Marie—4 in, 5 in, 9 in; Angle—7 in, 5 in, 6 in; and Chloe—3 in, 7 in, 5 in. Who among them was not able to make a triangle?

• Xylie

• Marie

• Angel

• Chloe

In ∆TRU, TR = 8 cm, RU = 9 cm, and TU = 10 cm. List the angles in order from least to greatest measure.

• m∠T, m∠R, m∠U

• m∠U, m∠T, m∠R

• m∠R, m∠T, m∠U

• m∠U, m∠R, m∠T

What is the range of the values of the diagonal d of a lot shaped like a parallelogram if adjacent sides are 10 inches and 14 inches?

• 4 ≥ d ≥ 24

• 4 < d < 24

• 4 ≤ d ≤ 24

• 4 > d > 24

Find the range of possible measures for the third side of a triangle if two sides are 9 and 5

The side lengths of a non-degenerate \triangle ABC

△ABC are 4, 11

4,11 and c.

Which of the following is a possible value of c

• 15

• 7

• 17

• 12

If the measures of length of sides of a triangle are p, 2p and 3p, then what is the range of p?

• p>3

• 3<p<5

• p>2

• cannot be defined