Math Gr 9 Ch 12: Develop and use Theorem of Pythagores
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Questions and Answers

What is the longest side in a right-angled triangle?

  • The side adjacent to the acute angle
  • The side opposite the right angle (correct)
  • The side opposite the acute angle
  • The side adjacent to the right angle

    • What is the condition for a triangle to be acute-angled?

  • One angle is greater than 90 degrees
  • One angle is 90 degrees
  • All angles are equal to 90 degrees
  • All angles are less than 90 degrees (correct)

    • What is the formula to find the length of the hypotenuse in a right-angled triangle?

  • c = a^2 * b^2
  • c = a^2 + b^2
  • c = √(a^2 + b^2) (correct)
  • c = a + b

    • Which of the following triangles satisfies the condition a^2 + b^2 > c^2?

    <p>Acute-angled triangle</p> Signup and view all the answers

    What is the first step in using the Pythagorean theorem to find an unknown side?

    <p>Identify the sides</p> Signup and view all the answers

    What is the converse of the Pythagorean theorem?

    <p>If c^2 = a^2 + b^2, then the triangle is right-angled</p> Signup and view all the answers

    Which of the following is a key point about the Pythagorean theorem?

    <p>It only applies to right-angled triangles</p> Signup and view all the answers

    What can be concluded about a triangle if a^2 + b^2 < c^2?

    <p>The triangle is obtuse-angled</p> Signup and view all the answers

    What can be concluded about a triangle if it satisfies the condition a^2 + b^2 = c^2?

    <p>It is a right-angled triangle.</p> Signup and view all the answers

    In which type of triangle does the relationship a^2 + b^2 > c^2 hold?

    <p>Acute-angled triangle.</p> Signup and view all the answers

    What is the purpose of the Pythagorean theorem?

    <p>To find the length of the hypotenuse in a right-angled triangle.</p> Signup and view all the answers

    If a triangle satisfies the condition c^2 = a^2 + b^2, what can be concluded about the triangle?

    <p>It is a right-angled triangle.</p> Signup and view all the answers

    What is the name of the theorem that states a^2 + b^2 = c^2 in a right-angled triangle?

    <p>Pythagorean theorem.</p> Signup and view all the answers

    What is the relationship between the length of the hypotenuse and the lengths of the other two sides in a right-angled triangle?

    <p>The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.</p> Signup and view all the answers

    In which type of triangle is the hypotenuse always the longest side?

    <p>Right-angled triangle.</p> Signup and view all the answers

    What is the formula to find a side in a right-angled triangle, given the lengths of the other two sides?

    <p>a = √(c^2 - b^2).</p> Signup and view all the answers

    If a triangle has sides of length 3, 4, and x, which of the following can be concluded about the triangle?

    <p>The triangle is right-angled and x is the length of the hypotenuse.</p> Signup and view all the answers

    Which of the following is true about the relationship between the sides of an obtuse-angled triangle?

    <p>a^2 + b^2 &lt; c^2</p> Signup and view all the answers

    What can be concluded about a triangle if a^2 + b^2 = 2c^2?

    <p>The triangle is isosceles.</p> Signup and view all the answers

    If a triangle has sides of length 5, 12, and x, which of the following is true?

    <p>The triangle is right-angled and x is the length of the hypotenuse.</p> Signup and view all the answers

    Which of the following is a necessary condition for a triangle to be right-angled?

    <p>The sum of the squares of two sides is equal to the square of the third side.</p> Signup and view all the answers

    What can be concluded about a triangle if a^2 - b^2 = c^2?

    <p>The triangle is isosceles.</p> Signup and view all the answers

    If a triangle has sides of length 7, 24, and x, which of the following can be concluded about the triangle?

    <p>The triangle is right-angled and x is the length of the hypotenuse.</p> Signup and view all the answers

    Which of the following is a sufficient condition for a triangle to be acute-angled?

    <p>a^2 + b^2 &gt; c^2</p> Signup and view all the answers

    If a triangle has sides of length 3, 5, and x, which of the following is true?

    <p>The triangle is right-angled.</p> Signup and view all the answers

    What is the relationship between the length of the hypotenuse and the lengths of the other two sides in a right-angled triangle?

    <p>The square of the hypotenuse is equal to the sum of the squares of the other two sides.</p> Signup and view all the answers

    If a triangle satisfies the condition a^2 + b^2 > c^2, what can be concluded about the triangle?

    <p>The triangle is acute-angled.</p> Signup and view all the answers

    What is the purpose of the converse of the Pythagorean theorem?

    <p>To determine if a triangle is right-angled.</p> Signup and view all the answers

    If a triangle has sides of length 7, 24, and 25, which of the following can be concluded about the triangle?

    <p>The triangle is right-angled.</p> Signup and view all the answers

    What is the formula to find the length of a side in a right-angled triangle, given the lengths of the other two sides?

    <p>a = sqrt(c^2 - b^2)</p> Signup and view all the answers

    If a triangle satisfies the condition a^2 + b^2 < c^2, what can be concluded about the triangle?

    <p>The triangle is obtuse-angled.</p> Signup and view all the answers

    In which type of triangle is the Pythagorean theorem not applicable?

    <p>Obtuse-angled triangle.</p> Signup and view all the answers

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