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Lesson: Triangle Inequality

Video

12:37

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

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.

  • A equal to
  • Bgreater than
  • C less than

Q3:

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

  • A 5 , 2 , 8
  • B 2 , 5 , 6
  • C 5 , 3 , 8

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 ] 0 . 2 , 5 [
  • B [ 0 . 2 , 5 ]
  • C ] 0 , 5 [
  • D ] 2 , 2 [

Q6:

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

  • A 13 cm, 18 cm, and 43 cm
  • B 13 cm, 36 cm, and 43 cm
  • C 7 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 ] 6 , 1 2 [
  • B ] βˆ’ 6 , 1 2 [
  • C [ 6 , 1 2 ]
  • D ] 3 , 9 [

Q8:

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

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

Q9:

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

  • ANo
  • BYes
  • 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.

  • A true
  • B false

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 17 cm
  • B 21 cm
  • C 22 cm
  • D 19 cm

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.

  • A 1 7 < π‘₯ < 2 1
  • B 2 < π‘₯ < 2 1
  • C 2 3 < π‘₯ < 2 7
  • D 1 7 < π‘₯ < 2 5
  • E 2 9 < π‘₯ < 3 3

Q13:

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

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

Q14:

Is the following statement true or false: β€œThe 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?

  • Ayes
  • Bno

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 equal to
  • B less than
  • C greater than

Q17:

In triangle 𝐴 𝐡 𝐢 , is 𝐴 𝐡 + 𝐡 𝐢 βˆ’ 𝐴 𝐢 < , = , > 0 o r ?

  • A =
  • B >
  • C <

Q18:

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

  • Ano
  • Byes

Q19:

𝐴 𝐡 𝐢 is a triangle where 𝐹 is the midpoint of 𝐡 𝐢 . Is 𝐴 𝐡 + 𝐴 𝐢 < , = , > 𝐴 𝐹 + 𝐡 𝐹 o r ?

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

Q22:

𝐴 𝐡 𝐢 is a triangle where ( 𝐴 𝐡 ) > ( 𝐴 𝐢 ) + ( 𝐡 𝐢 )    , 𝐴 𝐡 = 2 9 c m , 𝐴 𝐢 = 2 2 . 2 c m ,  𝐴 𝐷 βŸ‚ βƒ–     βƒ— 𝐡 𝐢 at the point 𝐷 , and 𝐴 𝐷 = 2 1 c m . Calculate the length of 𝐡 𝐢 .

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.

  • A π‘₯ > βˆ’ 6
  • B π‘₯ > 1 0
  • C 8 < π‘₯ < 1 4
  • D 2 0 < π‘₯ < 2 2
  • E π‘₯ < βˆ’ 1 8

Q24:

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

  • A 3 < π‘₯ < 1 3
  • B √ 3 9 < π‘₯ < √ 8 9
  • C π‘₯ < 1 3
  • D π‘₯ = √ 8 9
  • E π‘₯ > 3

Q25:

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

  • A 2 , 5 , 8
  • B 5 , 3 , 6
  • C 2 , 5 , 7
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