Understanding properties of triangles

Two side measures of a triangle are given. What is the range of values for the third side?

8 and 9

• 5 < x < 17

• 5 < x < 13

• 2 < x < 17

• 1 < x < 17

Find the length of the missing side.

• 7

• 6.3

• 2.5

• 9

The Triangle Inequality Theorem says: The ​ (a)   of any two side lengths of a triangle is ​ (b)   than the third side length.

• sum
• greater
• difference
• less

Two side measures of a triangle are given. What is the range of values for the third side?

9 and 7

• 6 < x < 14

• 2 < x < 13

• 2 < x < 16

• 2 < x < 15

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

• more than 6 but less than 20
• more than 20 but less than 6
• less than 6 but more than 20

The lengths of two sides of a triangle are 5 in and 16 in. What is the range of possible lengths for the third side?

• 11 in < x < 21 in

• x > 0

• 11 or 21

• 5 < x < 16

Two lengths of a triangle are 25 and 25. What are the possible values for the third side of the triangle?

• 0 < x < 50
• 12.5 < x < 50
• 1 < x < 49
• 0 < x < 49

If the longest side of the triangle was 10. Then the two shorter sides must have a sum of ....?

• 9
• 10
• 11
• 8

If the sides of a triangle are 8, 12, and 16, what is the semi-perimeter?

• 8

• 18

• 24

• 36

The diagram shows the locations of Noah and Ben after swimming in different directions from a dock. Let d be the distance from Noah to Ben, in yards.

Which represents all the possible values, in yards, of d?

• $0<d<147$

• $0<d<105$

• $21<d<147$

• $63<d<84$