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

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

Q1:

In △𝐴𝐵𝐶, 𝑚∠𝐴=62∘ and 𝑚∠𝐵=92∘. Arrange the lengths of the sides of the triangle in descending order.

  • A𝐴𝐵,𝐴𝐶,𝐵𝐶
  • B𝐵𝐶,𝐴𝐵,𝐴𝐶
  • C𝐴𝐶,𝐵𝐶,𝐴𝐵
  • D𝐴𝐶,𝐴𝐵,𝐵𝐶
  • E𝐵𝐶,𝐴𝐶,𝐴𝐵

Q2:

From the figure, how do 𝐴𝐵 and 𝐵𝐶 compare?

  • A𝐴𝐵<𝐵𝐶
  • B𝐴𝐵=𝐵𝐶
  • C𝐴𝐵>𝐵𝐶

Q3:

Consider the shown triangle 𝐴𝐵𝐶.

Fill in the blank with >, <, or =: 𝐴𝐶𝐴𝐵.

  • A=
  • B<
  • C>

Fill in the blank with >, <, or =: 𝐴𝐵𝐵𝐷.

  • A=
  • B>
  • C<

Fill in the blank with >, <, or =: 𝐶𝐷𝐴𝐷.

  • A<
  • B=
  • C>

Fill in the blank with >, <, or =: 𝐵𝐷𝐴𝐶.

  • A=
  • B>
  • C<

Q4:

Consider the given diagram.

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

𝐴𝐶𝐴𝐵

  • A=
  • B>
  • C<

𝐴𝐵𝐵𝐶

  • A=
  • B>
  • C<

𝐷𝐶𝐴𝐷

  • A<
  • B=
  • C>

𝐴𝐷𝐴𝐶

  • A=
  • B>
  • C<

Q5:

In a triangle 𝐴𝐵𝐶, if 𝑚∠𝐵=90∘, which of the following is true?

  • A𝐵𝐶>𝐴𝐶
  • B𝐴𝐵>𝐴𝐶
  • C𝐴𝐶>𝐴𝐵
  • D𝐴𝐵=𝐴𝐶

Q6:

From the figure, fill in the blank with either >, <, or =: 𝐴𝐶𝐵𝐶.

  • A<
  • B=
  • C>

Q7:

Consider the figure shown.

Fill in the blank with >, <, or =: 𝐴𝐶𝐶𝐷.

  • A=
  • B>
  • C<

Q8:

Consider the figure shown.

Fill in the blank with >, <, or =: 𝐴𝐵𝐵𝐶.

  • A>
  • B=
  • C<

Q9:

Consider the shown figure.

Fill in the blank using >, <, or =: 𝐴𝐵𝐶𝐷.

  • A<
  • B>
  • C=

Q10:

True or False: The longest side of a triangle is opposite to the angle with the largest measure.

  • AFalse
  • BTrue

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