Lesson Worksheet: Inequalities in One Triangle Mathematics

In this worksheet, we will practice recognizing the properties of inequalities and their relation to the sides of a triangle and implementing them on the measures of its angles.


Complete the following using <, =, or >: If, in the triangle 𝐷𝐸𝐹, 𝐷𝐸>𝐸𝐹, then 𝑚𝐹𝑚𝐷.

  • A=
  • B>
  • C<


Suppose that, in triangle 𝐴𝐵𝐶, 𝐴𝐵=20, 𝐵𝐶=18, and 𝐴𝐶=8. Arrange the measures of the angles in descending order.

  • A𝑚𝐶,𝑚𝐵,𝑚𝐴
  • B𝑚𝐴,𝑚𝐵,𝑚𝐶
  • C𝑚𝐶,𝑚𝐴,𝑚𝐵
  • D𝑚𝐴,𝑚𝐶,𝑚𝐵


Suppose that, in triangle 𝐴𝐵𝐶, 𝐴𝐵=18cm, 𝐵𝐶=19cm, and 𝐴𝐶=14cm. Arrange the measures of the angles in ascending order.

  • A𝑚𝐴,𝑚𝐵,𝑚𝐶
  • B𝑚𝐵,𝑚𝐶,𝑚𝐴
  • C𝑚𝐶,𝑚𝐴,𝑚𝐵
  • D𝑚𝐶,𝑚𝐵,𝑚𝐴


In a triangle 𝐷𝐸𝐹 where 𝐷𝐸=𝐷𝐹, which angle has the same measure as 𝐸?

  • A𝐹
  • B𝐷


Use <, =, or > to fill in the blank: If 𝑋𝐶>𝑋𝐵, then 𝑚𝐴𝐵𝑋𝑚𝐷𝐶𝑋.

  • A>
  • B<
  • C=


Use <, =, or > to complete the following: If 𝐴𝐵>𝐴𝐶, then 𝑚𝐴𝐸𝐷𝑚𝐴𝐷𝐸.

  • A=
  • B>
  • C<


Arrange the measures of the angles of triangle 𝐴𝐵𝐶 in ascending order, given that 𝐴𝐵=5.9cm, 𝐵𝐶=8.4cm, and 𝐴𝐶=4.6cm.

  • A𝑚𝐶,𝑚𝐵,𝑚𝐴
  • B𝑚𝐵,𝑚𝐶,𝑚𝐴
  • C𝑚𝐴,𝑚𝐵,𝑚𝐶
  • D𝑚𝐶,𝑚𝐴,𝑚𝐵


Arrange the sides 𝐶𝐷, 𝐴𝐶, 𝐶𝐵, and 𝐴𝐷 in decreasing order of length.

  • A𝐴𝐷, 𝐶𝐵, 𝐶𝐷, 𝐴𝐶
  • B𝐴𝐷, 𝐶𝐵, 𝐴𝐶, 𝐶𝐷
  • C𝐶𝐵, 𝐴𝐷, 𝐴𝐶, 𝐶𝐷
  • D𝐴𝐶, 𝐶𝐷, 𝐶𝐵, 𝐴𝐷
  • E𝐴𝐶, 𝐶𝐷, 𝐴𝐷, 𝐶𝐵


In the figure, 𝐴𝐵>𝐵𝐶 and 𝐴𝐷>𝐷𝐶. Which of the following is true?

  • A𝑚𝐴𝐶𝐷>𝑚𝐴𝐵𝐶
  • B𝑚𝐵𝐶𝐷>𝑚𝐵𝐴𝐷
  • C𝑚𝐵𝐶𝐷=𝑚𝐵𝐴𝐷
  • D𝑚𝐵𝐶𝐴<𝑚𝐵𝐴𝐶
  • E𝑚𝐵𝐶𝐷<𝑚𝐵𝐴𝐷


Which of the following inequalities describes the angles of triangle 𝐴𝐵𝐶?

  • A𝑚𝐵>𝑚𝐴>𝑚𝐶
  • B𝑚𝐴>𝑚𝐵>𝑚𝐶
  • C𝑚𝐵>𝑚𝐶>𝑚𝐴
  • D𝑚𝐶>𝑚𝐵>𝑚𝐴
  • E𝑚𝐶>𝑚𝐴>𝑚𝐵

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