# Worksheet: Inequality in One Triangle: Sides

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

Q1:

In what interval must the length of lie? • A
• B
• C
• D

Q2:

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

• Aless than
• Bequal to
• Cgreater than

Q3:

Which of the following lists could be the lengths of sides of a triangle?

• A
• B
• C

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?

• A7 cm, 36 cm, and 43 cm
• B13 cm, 18 cm, and 43 cm
• C13 cm, 36 cm, and 43 cm

Q7:

If the lengths of two sides of a triangle are 3 cm and 9 cm, determine the smallest 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.
• BNo
• CYes

Q9:

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

• AYes
• BNo
• CThere is not enough information to tell.

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.

• Atrue
• Bfalse

Q11:

If the measures of two sides of a triangle are 10 cm and 26 cm, which of the following could NOT be the measure of the third side?

• A21 cm
• B32 cm
• C34 cm
• D36 cm
• E18 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?

• A19 cm, 1 cm, 8 cm
• B4 cm, 18 cm, 3 cm
• C11 cm, 11 cm, 4 cm
• D18 cm, 7 cm, 5 cm

Q14:

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

• Afalse
• Btrue

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?

• Aequal to
• Bgreater than
• Cless 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 4.1 cm and 7.8 cm, then the length of the third is between and .

• A4.1 cm, 7.8 cm
• B4.7 cm, 10.9 cm
• C3.7 cm, 11.9 cm
• D2.7 cm, 12.9 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

Q25:

Which of the following lists could be the lengths of sides of a triangle?

• A
• B
• C