What is the Pythagorean Theorem?
Pythagorean Theorem

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•
Mathematics
•
10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².
2.
FLASHCARD QUESTION
Front
If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.
3.
FLASHCARD QUESTION
Front
What is the length of the missing side if the hypotenuse is 13 and one side is 5?
Back
Using the Pythagorean Theorem: 13² = 5² + b². Thus, 169 = 25 + b², which gives b² = 144. Therefore, b = √144 = 12.
4.
FLASHCARD QUESTION
Front
In a right triangle, if the lengths of the two legs are equal, what is the relationship between the legs and the hypotenuse?
Back
If the legs are equal (let's say both are 'a'), then the hypotenuse (c) can be calculated as c = a√2.
5.
FLASHCARD QUESTION
Front
What is the distance formula derived from the Pythagorean Theorem?
Back
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).
6.
FLASHCARD QUESTION
Front
If a right triangle has a hypotenuse of 15 and one leg of 9, what is the length of the other leg?
Back
Using the Pythagorean Theorem: 15² = 9² + b². Thus, 225 = 81 + b², which gives b² = 144. Therefore, b = √144 = 12.
7.
FLASHCARD QUESTION
Front
What is the relationship between the sides of a 30-60-90 triangle?
Back
In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is 'x', the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.
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