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.


Complete the following using <, =, or >: If, in the triangle 𝐷𝐸𝐹, 𝐷𝐸>𝐸𝐹, then π‘šβˆ πΉπ‘šβˆ π·.

  • A=
  • B>
  • C<


Which is the correct relationship?

  • Aπ‘šβˆ π΅>π‘šβˆ πΆ
  • Bπ‘šβˆ π΅=π‘šβˆ πΆ
  • Cπ‘šβˆ π΅<π‘šβˆ πΆ


Consider this triangle.

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

π‘šβˆ π΄π‘šβˆ π΅

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

π‘šβˆ π΅π‘šβˆ πΆ

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

π‘šβˆ πΆπ‘šβˆ π΄

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


Given 𝐴𝐡=92cm, 𝐴𝐢=91cm, and 𝐢𝐸=𝐡𝐷, choose the correct relationship between π‘šβˆ π΄πΈπ· and π‘šβˆ π΄π·πΈ.

  • Aπ‘šβˆ π΄πΈπ·=π‘šβˆ π΄π·πΈ
  • Bπ‘šβˆ π΄πΈπ·<π‘šβˆ π΄π·πΈ
  • Cπ‘šβˆ π΄πΈπ·>π‘šβˆ π΄π·πΈ


From the figure, what is the relation between π‘šβˆ π΄π΅π· and π‘šβˆ π΄πΆπ·?

  • Aπ‘šβˆ π΄π΅π·<π‘šβˆ π΄πΆπ·
  • Bπ‘šβˆ π΄π΅π·=π‘šβˆ π΄πΆπ·
  • Cπ‘šβˆ π΄π΅π·>π‘šβˆ π΄πΆπ·


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

  • Aπ‘šβˆ π΅>π‘šβˆ π΄>π‘šβˆ πΆ
  • Bπ‘šβˆ π΄>π‘šβˆ π΅>π‘šβˆ πΆ
  • Cπ‘šβˆ π΅>π‘šβˆ πΆ>π‘šβˆ π΄
  • Dπ‘šβˆ πΆ>π‘šβˆ π΅>π‘šβˆ π΄
  • Eπ‘šβˆ πΆ>π‘šβˆ π΄>π‘šβˆ π΅


In the figure, 𝐴𝐡>𝐡𝐢 and 𝐴𝐷>𝐷𝐢. Which of the following is true?

  • Aπ‘šβˆ π΄πΆπ·>π‘šβˆ π΄π΅πΆ
  • Bπ‘šβˆ π΅πΆπ·>π‘šβˆ π΅π΄π·
  • Cπ‘šβˆ π΅πΆπ·=π‘šβˆ π΅π΄π·
  • Dπ‘šβˆ π΅πΆπ΄<π‘šβˆ π΅π΄πΆ
  • Eπ‘šβˆ π΅πΆπ·<π‘šβˆ π΅π΄π·


Given that 𝐴𝑀 is a median of triangle 𝐴𝐡𝐢 and that 𝐡𝑀<𝐴𝑀, what type of angle is ∠𝐡𝐴𝐢?

  • AReflex
  • BRight
  • CObtuse
  • DAcute


In △𝐴𝐡𝐢, 𝐡𝑀 bisects ∠𝐴𝐡𝐢, 𝐢𝑀 bisects ∠𝐴𝐢𝐡, and 𝐴𝐡>𝐴𝐢. If π‘šβˆ π‘€πΆπ΅=30∘, which of the following values can satisfy π‘šβˆ π‘€π΅πΆ?

  • A28∘
  • B32∘
  • C30∘


Use <, =, or > to fill in the blank: π‘šβˆ π΄π΅πΈπ‘šβˆ π΄πΆπ·.

  • A<
  • B=
  • C>

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