Pythagorean theorem and its applications.

Flashcard
•
Mathematics
•
8th Grade
•
Hard
+3
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 is expressed as: a² + b² = c².
Tags
CCSS.8.G.B.8
2.
FLASHCARD QUESTION
Front
What is the formula to find the length of side 'a' in a right triangle if 'b' and 'c' are known?
Back
The formula to find the length of side 'a' is: a = √(c² - b²).
Tags
CCSS.8.G.B.7
3.
FLASHCARD QUESTION
Front
If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?
Back
Using the Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Tags
CCSS.8.G.B.7
4.
FLASHCARD QUESTION
Front
What is the area of a square with a side length of 6 cm?
Back
The area of a square is calculated as side². Therefore, area = 6² = 36 cm².
Tags
CCSS.3.MD.C.7B
CCSS.4.MD.A.3
5.
FLASHCARD QUESTION
Front
In a right triangle, if one leg is 12 cm and the hypotenuse is 15 cm, what is the length of the other leg?
Back
Using the Pythagorean theorem: b = √(c² - a²) = √(15² - 12²) = √(225 - 144) = √81 = 9 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.
Tags
CCSS.HSG.CO.C.10
7.
FLASHCARD QUESTION
Front
How do you calculate the distance from a point to a line using the Pythagorean theorem?
Back
To calculate the distance from a point to a line, drop a perpendicular from the point to the line, forming a right triangle. Use the Pythagorean theorem to find the length of the perpendicular.
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