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In this lesson, we will learn how to apply the triangle inequality to determine whether three given lengths can be sides of a triangle.

Q1:

In what interval must the length of lie?

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

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.

Q8:

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

Q9:

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

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.

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?

Q12:

Find the range of all possible values of π₯ if ( π₯ + 6 ) cm, 2 cm, and 25 cm represent the lengths of the sides of a triangle.

Q13:

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

Q14:

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

Q15:

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

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?

Q17:

In triangle π΄ π΅ πΆ , is π΄ π΅ + π΅ πΆ β π΄ πΆ < , = , > 0 o r ?

Q18:

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

Q19:

π΄ π΅ πΆ is a triangle where πΉ is the midpoint of π΅ πΆ . Is π΄ π΅ + π΄ πΆ < , = , > π΄ πΉ + π΅ πΉ o r ?

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 .

Q22:

π΄ π΅ πΆ is a triangle where ( π΄ π΅ ) > ( π΄ πΆ ) + ( π΅ πΆ ) ο¨ ο¨ ο¨ , π΄ π΅ = 2 9 c m , π΄ πΆ = 2 2 . 2 c m , ο« π΄ π· β β ο© ο© ο© ο© β π΅ πΆ at the point π· , and π΄ π· = 2 1 c m . Calculate the length of π΅ πΆ .

Q23:

Write an inequality that describes all the values of π₯ such that a triangle with edge lengths ( π₯ + 8 ) cm, ( π₯ + 1 2 ) cm, and ( π₯ + 1 4 ) cm exists.

Q24:

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

Q25:

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