Gr12 Mathematics: Ch 7.5 Pythagorean Theorem
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Questions and Answers

What is the Pythagorean Theorem a fundamental principle of?

  • Algebra
  • Trigonometry
  • Calculus
  • Geometry (correct)

    • In the Pythagorean Theorem, what is the angle of the given triangle?

  • 45°
  • 60°
  • 120°
  • 90° (correct)

    • What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

  • To prove the theorem
  • To find the area of the triangle
  • To find the sum of the squares
  • To form similar triangles (correct)

    • What is the criterion used to show that ∆ABD is similar to ∆CBA?

    <p>AAA similarity criterion</p> Signup and view all the answers

    What is the formula for the area of a triangle?

    <p>Area = (1/2) × base × height</p> Signup and view all the answers

    What is the converse of the Pythagorean Theorem?

    <p>If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.</p> Signup and view all the answers

    What is true about triangles with equal heights?

    <p>They have proportional areas to their bases</p> Signup and view all the answers

    What is true about triangles with equal bases between the same parallel lines?

    <p>They have equal areas</p> Signup and view all the answers

    What is the relationship between the square on the hypotenuse and the squares on the other two sides in a right-angled triangle?

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

    What is the purpose of constructing ∆CAD and ∆ABD in the proof of the Pythagorean Theorem?

    <p>To prove that ∆CAD is similar to ∆ABD</p> Signup and view all the answers

    If the square of one side of a triangle is equal to the sum of the squares of the other two sides, what can be concluded?

    <p>The angle included by the other two sides is a right angle</p> Signup and view all the answers

    What is the relationship between the areas of triangles with equal heights?

    <p>They are proportional to their bases</p> Signup and view all the answers

    What is true about the similarity of ∆CAD and ∆CBA in the proof of the Pythagorean Theorem?

    <p>They are similar triangles by AAA similarity criterion</p> Signup and view all the answers

    What is the formula for the area of a triangle, given the base and height?

    <p>Area = 1/2 × base × height</p> Signup and view all the answers

    What can be concluded if ∆ABC is a right-angled triangle and AC^2 = AB × BC?

    <p>AC is the hypotenuse of the triangle</p> Signup and view all the answers

    What is the relationship between the areas of triangles with equal bases between the same parallel lines?

    <p>They are equal in area</p> Signup and view all the answers

    What is the significance of ∠A1 = ∠C in the proof of the Pythagorean Theorem?

    <p>It shows that ∆CAD is similar to ∆CBA</p> Signup and view all the answers

    What is the purpose of adding the results in steps 3 and 4 of the proof?

    <p>To prove that BC^2 = AB^2 + AC^2</p> Signup and view all the answers

    What is the implication of the converse of the Pythagorean Theorem?

    <p>If the square of one side is equal to the sum of the squares of the other two sides, then the angle included by these two sides is a right angle</p> Signup and view all the answers

    What is the reason for constructing ∆CAD and ∆ABD in the proof?

    <p>To establish the similarity between ∆CAD and ∆CBA, and ∆ABD and ∆CBA</p> Signup and view all the answers

    What can be concluded about ∆ABC if AC^2 = AB × BC?

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

    What is the relationship between the areas of ∆CAD and ∆CBA?

    <p>They are proportional to their bases</p> Signup and view all the answers

    What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

    <p>To construct ∆CAD and ∆ABD, which are similar to ∆CBA</p> Signup and view all the answers

    What is the significance of BC^2 = BD × BC + CB × DC in the proof?

    <p>It proves that the square of one side is equal to the sum of the squares of the other two sides</p> Signup and view all the answers

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