Podcast
Questions and Answers
What is the Pythagorean Theorem a fundamental principle of?
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?
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?
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?
What is the criterion used to show that ∆ABD is similar to ∆CBA?
What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
What is the converse of the Pythagorean Theorem?
What is the converse of the Pythagorean Theorem?
What is true about triangles with equal heights?
What is true about triangles with equal heights?
What is true about triangles with equal bases between the same parallel lines?
What is true about triangles with equal bases between the same parallel lines?
What is the relationship between the square on the hypotenuse and the squares on the other two sides in a right-angled triangle?
What is the relationship between the square on the hypotenuse and the squares on the other two sides in a right-angled triangle?
What is the purpose of constructing ∆CAD and ∆ABD in the proof of the Pythagorean Theorem?
What is the purpose of constructing ∆CAD and ∆ABD in the proof of the Pythagorean Theorem?
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?
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?
What is the relationship between the areas of triangles with equal heights?
What is the relationship between the areas of triangles with equal heights?
What is true about the similarity of ∆CAD and ∆CBA in the proof of the Pythagorean Theorem?
What is true about the similarity of ∆CAD and ∆CBA in the proof of the Pythagorean Theorem?
What is the formula for the area of a triangle, given the base and height?
What is the formula for the area of a triangle, given the base and height?
What can be concluded if ∆ABC is a right-angled triangle and AC^2 = AB × BC?
What can be concluded if ∆ABC is a right-angled triangle and AC^2 = AB × BC?
What is the relationship between the areas of triangles with equal bases between the same parallel lines?
What is the relationship between the areas of triangles with equal bases between the same parallel lines?
What is the significance of ∠A1 = ∠C in the proof of the Pythagorean Theorem?
What is the significance of ∠A1 = ∠C in the proof of the Pythagorean Theorem?
What is the purpose of adding the results in steps 3 and 4 of the proof?
What is the purpose of adding the results in steps 3 and 4 of the proof?
What is the implication of the converse of the Pythagorean Theorem?
What is the implication of the converse of the Pythagorean Theorem?
What is the reason for constructing ∆CAD and ∆ABD in the proof?
What is the reason for constructing ∆CAD and ∆ABD in the proof?
What can be concluded about ∆ABC if AC^2 = AB × BC?
What can be concluded about ∆ABC if AC^2 = AB × BC?
What is the relationship between the areas of ∆CAD and ∆CBA?
What is the relationship between the areas of ∆CAD and ∆CBA?
What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?
What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?
What is the significance of BC^2 = BD × BC + CB × DC in the proof?
What is the significance of BC^2 = BD × BC + CB × DC in the proof?
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