1. The prerequisite condition for the Pythagorean theorem formula $a^2 + b^2 = c^2$ is:
- A. The triangle is an isosceles triangle
- B. The triangle is a right triangle
- C. The triangle is an acute triangle
- D. Applies to any shape of triangle
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Pythagorean Theorem - Practice
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The prerequisite condition for the Pythagorean theorem formula a2+b2=c2 is:
Pythagorean Theorem - Practice - Quiz Questions
Test your mastery of the Pythagorean theorem formula, geometric background, and special cases.
2. Given a right triangle with two legs of $6$ and $8$, the length of the hypotenuse is:
- A. $10$
- B. $14$
- C. $48$
- D. $7$
3. Which of the following sets of values can form the side lengths of a right triangle (Pythagorean triple)?
- A. $1, 2, 3$
- B. $3, 4, 5$
- C. $5, 5, 10$
- D. $2, 2, 4$
4. In the "Rearrangement Proof" demonstrated in this experiment, the physical/geometric quantity that remains unchanged is:
- A. The position of the triangles
- B. The shape of the central blank area
- C. The total area and the sum of the areas of the four triangles
- D. The value of the hypotenuse $c$
5. In ancient China, the Pythagorean theorem was also known as the "Shang Gao Theorem". Which work recorded the dialogue about this theorem?
- A. The Nine Chapters on the Mathematical Art
- B. Suan Jing Shi Shu
- C. Zhou Bi Suan Jing
- D. Sea Island Mathematical Manual
6. [Calculation] One leg of a right triangle is $5$ and the hypotenuse is $13$. The length of the other leg is:
- A. $8$
- B. $12$
- C. $18$
- D. $\sqrt{194}$
7. In a right triangle, the hypotenuse $c$ is always:
- A. Equal to half of $a + b$
- B. Longer than any single leg
- C. Less than the median of the legs
- D. None of the above
8. If the three sides of a triangle satisfy $a^2 + b^2 = c^2$, then the triangle must be a right triangle. This proposition is called:
- A. Converse of the Pythagorean theorem
- B. Corollary of the Pythagorean theorem
- C. Axiomatization of the Pythagorean theorem
- D. Euclid's fifth postulate
9. [Experiment Design] In this simulation, if the side length $a$ is set to $150$ and $b$ is set to $200$, the displayed value of $c$ should be approximately:
- A. $250$
- B. $350$
- C. $300$
- D. $225$
10. The Pythagorean theorem reflects the harmonious unity between which two categories of mathematical concepts?
- A. Algebra and Geometry
- B. Integers and Fractions
- C. Dynamic and Static
- D. Logic and Intuition