Flashcards on Pythagorean theorem
Pythagorean Theorem Explained: Summary, Proof, & Applications
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Pythagorean Theorem
28 cards
Card 1
Question: What does the Pythagorean theorem establish a relationship between?
Answer: The lengths of the sides of a right-angled triangle.
Card 2
Question: What is a right-angled triangle?
Answer: A triangle in which one of the angles measures exactly 90 degrees.
Card 3
Question: Who is the Pythagorean theorem named after?
Answer: The ancient Greek mathematician Pythagoras.
Card 4
Question: In a right-angled triangle, what is the hypotenuse?
Answer: The side opposite the right angle.
Card 5
Question: How is the Pythagorean theorem expressed algebraically, if 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse?
Answer: a² + b² = c²
Card 6
Question: What do 'a' and 'b' represent in the Pythagorean theorem formula (a² + b² = c²)?
Answer: The lengths of the sides that form the right angle (the legs).
Card 7
Question: What does 'c' represent in the Pythagorean theorem formula (a² + b² = c²)?
Answer: The length of the longest side, which is always opposite the right angle (the hypotenuse).
Card 8
Question: Which side in the Pythagorean theorem formula (a² + b² = c²) is always the hypotenuse?
Answer: c
Card 9
Question: Describe the core idea of the proof by rearrangement of squares for the Pythagorean theorem.
Answer: It shows that the areas of the squares built on the two legs of a right triangle can be perfectly rearranged to form the area of the square built on t
Card 10
Question: If a right-angled triangle has legs of length 'a' and 'b' and a hypotenuse of length 'c', what are the areas of the squares constructed on each side?
Answer: a², b², and c²