Pythagorean Theorem

Flashcard
•
Mathematics
•
10th Grade
•
Hard
+2
Standards-aligned
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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 can be expressed as: c² = a² + b².
Tags
CCSS.8.G.B.8
2.
FLASHCARD QUESTION
Front
What are the legs of a right triangle?
Back
The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.
3.
FLASHCARD QUESTION
Front
If one leg of a right triangle is 5 cm and the other leg is 12 cm, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.
Tags
CCSS.8.G.B.7
4.
FLASHCARD QUESTION
Front
What is the length of the missing side if the hypotenuse is 10 cm and one leg is 6 cm?
Back
Using the Pythagorean Theorem: 10² = 6² + b². Thus, 100 = 36 + b², so b² = 64, and b = √64 = 8 cm.
Tags
CCSS.8.G.B.8
5.
FLASHCARD QUESTION
Front
In a right triangle, if the hypotenuse is 15 cm and one leg is 9 cm, what is the length of the other leg?
Back
Using the Pythagorean Theorem: 15² = 9² + b². Thus, 225 = 81 + b², so b² = 144, and b = √144 = 12 cm.
Tags
CCSS.8.G.B.7
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. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.
Tags
CCSS.HSG.CO.C.10
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.
Tags
CCSS.8.G.B.8
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