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

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 △𝐴𝐡𝐢, π‘šβˆ π΄=62∘ and π‘šβˆ π΅=92∘. Arrange the lengths of the sides of the triangle in descending order.

  • A𝐴𝐡,𝐴𝐢,𝐡𝐢
  • B𝐡𝐢,𝐴𝐡,𝐴𝐢
  • C𝐴𝐢,𝐡𝐢,𝐴𝐡
  • D𝐴𝐢,𝐴𝐡,𝐡𝐢
  • E𝐡𝐢,𝐴𝐢,𝐴𝐡

Q2:

From the figure, how do 𝐴𝐡 and 𝐡𝐢 compare?

  • A𝐴𝐡<𝐡𝐢
  • B𝐴𝐡=𝐡𝐢
  • C𝐴𝐡>𝐡𝐢

Q3:

Consider the shown triangle 𝐴𝐡𝐢.

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

  • A=
  • B<
  • C>

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

  • A=
  • B>
  • C<

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

  • A<
  • B=
  • C>

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

  • A=
  • B>
  • C<

Q4:

Consider the given diagram.

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

𝐴𝐢𝐴𝐡

  • A=
  • B>
  • C<

𝐴𝐡𝐡𝐢

  • A=
  • B>
  • C<

𝐷𝐢𝐴𝐷

  • A<
  • B=
  • C>

𝐴𝐷𝐴𝐢

  • A=
  • B>
  • C<

Q5:

In a triangle 𝐴𝐡𝐢, if π‘šβˆ π΅=90∘, which of the following is true?

  • A𝐡𝐢>𝐴𝐢
  • B𝐴𝐡>𝐴𝐢
  • C𝐴𝐢>𝐴𝐡
  • D𝐴𝐡=𝐴𝐢

Q6:

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

  • A<
  • B=
  • C>

Q7:

Consider the figure shown.

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

  • A=
  • B>
  • C<

Q8:

Consider the figure shown.

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

  • A>
  • B=
  • C<

Q9:

Consider the shown figure.

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

  • 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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