Worksheet: Pythagorean Inequality Theorem

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

Q1:

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

  • Aacute
  • Bright
  • Cobtuse

Q2:

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

  • Aacute
  • Bright
  • Cobtuse

Q3:

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

  • Aright
  • Bacute
  • Cobtuse

Q4:

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

  • Aacute
  • Bright
  • Cobtuse

Q5:

Determine whether △𝐡𝐢𝐷 is an obtuse or acute triangle.

  • Aobtuse
  • Bacute

Q6:

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

Q7:

In △𝐴𝐡𝐢, suppose that (𝐴𝐡)+(𝐡𝐢)=72.25 and 𝐴𝐢=8.5 what kind of angle is ∠𝐡?

  • Aobtuse
  • Bacute
  • Cright

Q8:

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

  • A∠𝐴
  • B∠𝐡
  • C∠𝐢

Q9:

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

  • Aan acute-angled triangle
  • Ba right-angled triangle
  • Can obtuse-angled triangle

Q10:

Consider △𝐴𝐡𝐢, where 𝐴𝐡=13, 𝐡𝐢=14, and 𝐴𝐢=6. Is ∠𝐴an acute angle?

  • AYes
  • BNo

Q11:

Consider △𝐴𝐡𝐢, where 𝐴𝐡=8, 𝐡𝐢=10, and 𝐴𝐢=6. Is ∠𝐴 a right angle?

  • AYes
  • BNo

Q12:

Consider △𝐴𝐡𝐢, where 𝐴𝐡=7, 𝐡𝐢=12, and 𝐴𝐢=8. Is ∠𝐴 an obtuse angle?

  • ANo
  • BYes

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