# Worksheet: Triangle Inequality

In this worksheet, we will practice applying the triangle inequality to determine whether three given lengths can be sides of a triangle.

**Q2: **

Complete the sentence: The sum of the lengths of any two sides in a triangle is the length of the other side.

- A less than
- B equal to
- Cgreater than

**Q4: **

Which of the following lists of numbers is NOT the lengths of sides of a triangle?

- A
- B
- C
- D

**Q5: **

Two sides in a triangle have lengths 2.6 and 2.4. In what interval must the length of the third side be?

- A
- B
- C
- D

**Q6: **

Which of the following could be side lengths of a triangle?

- A 7 cm, 36 cm, and 43 cm
- B 13 cm, 18 cm, and 43 cm
- C 13 cm, 36 cm, and 43 cm

**Q7: **

If the lengths of two sides of a triangle are 3 cm and 9 cm, determine the interval to which the length of the third side belongs.

- A
- B
- C
- D

**Q8: **

Is it possible to form a triangle with side lengths 6 m, 7 m, and 18 m?

- AThere is not enough information to tell.
- BYes
- CNo

**Q9: **

Is it possible to form a triangle with side lengths 3 inches, 5 inches, and 7 inches?

- AThere is not enough information to tell.
- BNo
- CYes

**Q10: **

Determine whether the following sentence is true or false: Knowing the measures of the angles of a triangle is enough to be able to draw that triangle.

- A false
- B true

**Q11: **

If the measures of two sides of a triangle are 3 cm and 20 cm, which of the following could NOT be the measure of the third side?

- A 19 cm
- B 21 cm
- C 22 cm
- D 17 cm

**Q12: **

Find the range of all possible values of if cm, 2 cm, and 25 cm represent the lengths of the sides of a triangle.

- A
- B
- C
- D
- E

**Q13: **

Which of the following groups of lengths can form the sides of a triangle?

- A 19 cm, 1 cm, 8 cm
- B 4 cm, 18 cm, 3 cm
- C 18 cm, 7 cm, 5 cm
- D 11 cm, 11 cm, 4 cm

**Q14: **

Is the following statement true or false: βThe longest side of a triangle is opposite to the angle with the largest measure.β

- Atrue
- Bfalse

**Q15: **

Does the triangle with side lengths 8, 32, and 16 exist?

- Ano
- Byes

**Q16: **

Is the length of any side in a triangle less than, equal to or greater than the sum of the length of the other two sides?

- A greater than
- B equal to
- C less than

**Q17: **

In triangle , is , , or ?

- A
- B
- C

**Q18: **

Is it possible to draw a triangle with side lengths of 6 cm, 11 cm, and 9 cm?

- Ayes
- Bno

**Q19: **

is a triangle where is the midpoint of . Is , , or ?

- A
- B
- C

**Q20: **

If the measures of two sides of a triangle are 5 feet and 12 feet, what is the least possible whole-number measure for the third side?

**Q21: **

If the two side lengths of a triangle are 19.2 cm and 13.3 cm, then the length of the third is between and .

- A 4.9 cm, 33.5 cm
- B 6.9 cm, 31.5 cm
- C 19.2 cm, 13.3 cm
- D 5.9 cm, 32.5 cm

**Q22: **

is a triangle where , , , at the point , and . Calculate the length of .

**Q23: **

Write an inequality that describes all the values of such that a triangle with edge lengths cm, cm, and cm exists.

- A
- B
- C
- D
- E

**Q24: **

A triangle has sides of lengths 5 cm, 8 cm, and cm. State the range of values that could take.

- A
- B
- C
- D
- E