Lesson Worksheet: Pythagorean Inequality Theorem Mathematics • 8th Grade

In this worksheet, we will practice determining whether an angle in a triangle is acute, right, or obtuse by using the Pythagorean inequality theorem.


In triangle 𝐴𝐡𝐢, (𝐴𝐡)+(𝐡𝐢)<(𝐴𝐢). What type of angle is 𝐡?

  • Aacute
  • Bright
  • Cobtuse


In triangle π‘‹π‘Œπ‘, (π‘Œπ‘)>(𝑋𝑍)βˆ’(π‘‹π‘Œ). What type of angle is π‘Œ?

  • Aright
  • Bacute
  • Cobtuse


In a triangle 𝐴𝐡𝐢, if (𝐴𝐡)=(𝐡𝐢)+(𝐴𝐢), which angle is the right angle?

  • A∠𝐴
  • B∠𝐡
  • C∠𝐢


Consider △𝐴𝐡𝐢, with 𝐴𝐡=9, 𝐡𝐢=10, and 𝐴𝐢=11. What kind of triangle is this, in terms of its angles?

  • AAn acute triangle
  • BA right triangle
  • CAn obtuse triangle


If 𝐴𝐡𝐢 is a triangle whose side lengths are 11 cm, 26.4 cm, and 28.6 cm and is similar to a triangle π‘‹π‘Œπ‘, determine the type of β–³π‘‹π‘Œπ‘ in terms of its angles.

  • Aacute
  • Bright
  • Cobtuse


Determine the type of △𝐡𝐢𝐷 in terms of its angles.

  • AObtuse triangle
  • BAcute triangle
  • CRight triangle


Triangle 𝐴𝐡𝐢 has side lengths 𝐴𝐡=7cm, 𝐡𝐢=9cm, and 𝐴𝐢=10cm.

Determine the angle with the greatest measure in △𝐴𝐡𝐢.

  • A∠𝐢
  • B∠𝐡
  • C∠𝐴

Determine the type of △𝐴𝐡𝐢 in terms of its angles.

  • ARight triangle
  • BAcute triangle
  • CObtuse triangle


𝐴𝐡𝐢𝐷 is a parallelogram. If 𝐴𝐢=13cm, 𝐴𝐷=13cm, and 𝐷𝐢=5cm, what is the type of △𝐴𝐷𝐢?

  • AAcute triangle
  • BRight triangle
  • CObtuse triangle


Given that 𝐴𝐢=12cm, 𝐡𝐢=6cm, and 𝐴𝐡=13cm, what type is the largest angle?

  • AObtuse
  • BAcute
  • CRight


Classify the triangle 𝐸𝐹𝐢, where 𝐡𝐹=√3cm and 𝐴𝐸=√6cm and where 𝐴𝐡𝐢𝐷 is a rectangle.

  • ARight triangle
  • BAcute triangle
  • CObtuse triangle

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