Lesson Worksheet: Inequalities in One Triangle Mathematics

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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.

Q1:

Complete the following using <, =, or >: If, in the triangle 𝐷𝐸𝐹, 𝐷𝐸>𝐸𝐹, then 𝑚∠𝐹𝑚∠𝐷.

  • A=
  • B>
  • C<

Q2:

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

  • A𝑚∠𝐶,𝑚∠𝐵,𝑚∠𝐴
  • B𝑚∠𝐴,𝑚∠𝐵,𝑚∠𝐶
  • C𝑚∠𝐶,𝑚∠𝐴,𝑚∠𝐵
  • D𝑚∠𝐴,𝑚∠𝐶,𝑚∠𝐵

Q3:

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

  • A𝑚∠𝐴,𝑚∠𝐵,𝑚∠𝐶
  • B𝑚∠𝐵,𝑚∠𝐶,𝑚∠𝐴
  • C𝑚∠𝐶,𝑚∠𝐴,𝑚∠𝐵
  • D𝑚∠𝐶,𝑚∠𝐵,𝑚∠𝐴

Q4:

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

  • A∠𝐹
  • B∠𝐷

Q5:

Use <, =, or > to fill in the blank: If 𝑋𝐶>𝑋𝐵, then 𝑚∠𝐴𝐵𝑋𝑚∠𝐷𝐶𝑋.

  • A>
  • B<
  • C=

Q6:

Use <, =, or > to complete the following: If 𝐴𝐵>𝐴𝐶, then 𝑚∠𝐴𝐸𝐷𝑚∠𝐴𝐷𝐸.

  • A=
  • B>
  • C<

Q7:

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

  • A𝑚∠𝐶,𝑚∠𝐵,𝑚∠𝐴
  • B𝑚∠𝐵,𝑚∠𝐶,𝑚∠𝐴
  • C𝑚∠𝐴,𝑚∠𝐵,𝑚∠𝐶
  • D𝑚∠𝐶,𝑚∠𝐴,𝑚∠𝐵

Q8:

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

Q9:

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

  • A𝑚∠𝐴𝐶𝐷>𝑚∠𝐴𝐵𝐶
  • B𝑚∠𝐵𝐶𝐷>𝑚∠𝐵𝐴𝐷
  • C𝑚∠𝐵𝐶𝐷=𝑚∠𝐵𝐴𝐷
  • D𝑚∠𝐵𝐶𝐴<𝑚∠𝐵𝐴𝐶
  • E𝑚∠𝐵𝐶𝐷<𝑚∠𝐵𝐴𝐷

Q10:

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

  • A𝑚∠𝐵>𝑚∠𝐴>𝑚∠𝐶
  • B𝑚∠𝐴>𝑚∠𝐵>𝑚∠𝐶
  • C𝑚∠𝐵>𝑚∠𝐶>𝑚∠𝐴
  • D𝑚∠𝐶>𝑚∠𝐵>𝑚∠𝐴
  • E𝑚∠𝐶>𝑚∠𝐴>𝑚∠𝐵

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