Lesson Worksheet: Inequality in One Triangle: Angle Comparison Mathematics • 11th Grade

In this worksheet, we will practice forming inequalities involving the measures of angles in a triangle given the lengths of the sides of the triangle.

Q1:

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

  • A=
  • B>
  • C<

Q2:

Which is the correct relationship?

  • A𝑚𝐵>𝑚𝐶
  • B𝑚𝐵=𝑚𝐶
  • C𝑚𝐵<𝑚𝐶

Q3:

Consider this triangle.

Fill in the blanks in the following statements using =, <, or >.

𝑚𝐴𝑚𝐵

  • A>
  • B<
  • C=
  • DThere is not enough information to determine the answer.

𝑚𝐵𝑚𝐶

  • A<
  • B=
  • C>
  • DThere is not enough information to determine the answer.

𝑚𝐶𝑚𝐴

  • A<
  • B=
  • C>
  • DThere is not enough information to determine the answer.

Q4:

Given 𝐴𝐵=92cm, 𝐴𝐶=91cm, and 𝐶𝐸=𝐵𝐷, choose the correct relationship between 𝑚𝐴𝐸𝐷 and 𝑚𝐴𝐷𝐸.

  • A𝑚𝐴𝐸𝐷=𝑚𝐴𝐷𝐸
  • B𝑚𝐴𝐸𝐷<𝑚𝐴𝐷𝐸
  • C𝑚𝐴𝐸𝐷>𝑚𝐴𝐷𝐸

Q5:

From the figure, what is the relation between 𝑚𝐴𝐵𝐷 and 𝑚𝐴𝐶𝐷?

  • A𝑚𝐴𝐵𝐷<𝑚𝐴𝐶𝐷
  • B𝑚𝐴𝐵𝐷=𝑚𝐴𝐶𝐷
  • C𝑚𝐴𝐵𝐷>𝑚𝐴𝐶𝐷

Q6:

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

Q7:

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

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

Q8:

Given that 𝐴𝑀 is a median of triangle 𝐴𝐵𝐶 and that 𝐵𝑀<𝐴𝑀, what type of angle is 𝐵𝐴𝐶?

  • AReflex
  • BRight
  • CObtuse
  • DAcute

Q9:

In 𝐴𝐵𝐶, 𝐵𝑀 bisects 𝐴𝐵𝐶, 𝐶𝑀 bisects 𝐴𝐶𝐵, and 𝐴𝐵>𝐴𝐶. If 𝑚𝑀𝐶𝐵=30, which of the following values can satisfy 𝑚𝑀𝐵𝐶?

  • A28
  • B32
  • C30

Q10:

Use <, =, or > to fill in the blank: 𝑚𝐴𝐵𝐸𝑚𝐴𝐶𝐷.

  • A<
  • B=
  • C>

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