Lesson Worksheet: Introduction to Inequalities in Triangles Mathematics

In this worksheet, we will practice defining the concept of inequality in general and the axioms of inequality and comparing between the measures of angles given in a triangle.

Q1:

Which of the following inequalities is correct?

  • A𝑚𝑋𝑌𝑍>𝑚𝑋𝑌𝑆>𝑚𝑋𝑍𝑌
  • B𝑚𝑋>𝑚𝑋𝑍𝑌>𝑚𝑋𝑌𝑍
  • C𝑚𝑋𝑌𝑆>𝑚𝑋𝑍𝑌>𝑚𝑋𝑌𝑍
  • D𝑚𝑋𝑍𝑇>𝑚𝑋>𝑚𝑋𝑍𝑌
  • E𝑚𝑋𝑍𝑌>𝑚𝑋𝑌𝑍>𝑚𝑋

Q2:

Is 𝑚𝐴𝐷𝑌<, =, or >𝑚𝐴𝐶𝐷?

  • A=
  • B<
  • C>

Q3:

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

  • A=
  • B<
  • C>

Q4:

Use <, =, or > to fill in the blank: Ifthen𝑚𝐴𝐵𝑀<𝑚𝐴𝐶𝑀,𝑚𝐴𝐵𝐶𝑚𝐴𝐶𝐵.

  • A=
  • B>
  • C<

Q5:

Which inequality is satisfied by this figure?

  • A𝑚𝐶<𝑚𝐵<𝑚𝐵𝐴𝐶
  • B𝑚𝐷𝐴𝐶<𝑚𝐵<𝑚𝐶
  • C𝑚𝐵<𝑚𝐵𝐴𝐶<𝑚𝐶
  • D𝑚𝐵𝐴𝐶<𝑚𝐶<𝑚𝐷𝐴𝐶
  • E𝑚𝐷𝐴𝐶<𝑚𝐵<𝑚𝐵𝐴𝐶

Q6:

Use <, =, or > to fill in the blank: If 𝑚𝐶𝐵𝐷=𝑚𝐶𝐷𝐵, then 𝑚𝐴𝐵𝐶𝑚𝐴𝐷𝐶.

  • A<
  • B=
  • C>

Q7:

Use <, =, or > to fill in the blank: If 𝑚𝐴𝐶𝐵>𝑚𝐴𝐵𝐶, then 𝑚𝐴𝐵𝑋𝑚𝐴𝐶𝑌.

  • A=
  • B<
  • C>

Q8:

Use <, =, or > to complete the statement: If 𝐴𝐵=62, 𝐴𝐶=63, and 𝑚𝐴𝑋𝑌=𝑚𝐴𝑌𝑋, then 𝑌𝐶𝑋𝐵.

  • A<
  • B=
  • C>

Q9:

Use <, =, or > to complete the statement: If 𝑚𝐴𝐶𝐵=62 and 𝑚𝐴=57, then 𝑚𝐴𝐵𝐷𝑚𝐴𝐶𝐷.

  • A=
  • B>
  • C<

Q10:

Complete using <, =, or >: If 𝑚𝐷𝐵𝐶=73 and 𝑚𝐶=37, then 𝑚𝐴𝐵𝐶𝑚𝐴𝐷𝐶.

  • A>
  • B<
  • C=

This lesson includes 9 additional questions and 90 additional question variations for subscribers.

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