Pythagorean Theorem Problems

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•
Mathematics
•
9th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Pythagorean Theorem?
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 is expressed as a² + b² = c².
2.
FLASHCARD QUESTION
Front
In a right triangle, which side is the hypotenuse?
Back
The hypotenuse is the longest side of a right triangle, opposite the right angle.
3.
FLASHCARD QUESTION
Front
If one side of a right triangle is 3 feet and the other side is 4 feet, what is the length of the hypotenuse?
Back
5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).
4.
FLASHCARD QUESTION
Front
What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?
Back
To find the length of a side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².
5.
FLASHCARD QUESTION
Front
How do you find the length of the diagonal of a rectangle?
Back
Use the Pythagorean Theorem: if the rectangle has a width (a) and height (b), the diagonal (d) is found using d = √(a² + b²).
6.
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.
7.
FLASHCARD QUESTION
Front
What is the relationship between the sides of a 45-45-90 triangle?
Back
In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.
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