Pythagoras
Flashcard
•
Mathematics
•
8th - 10th Grade
•
Practice Problem
•
Hard
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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.
2.
FLASHCARD QUESTION
Front
If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?
Back
5 units (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).
3.
FLASHCARD QUESTION
Front
What is the length of the hypotenuse if the two other sides are 5 m and 12 m?
Back
13 m (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169, so c = √169 = 13).
4.
FLASHCARD QUESTION
Front
What is the relationship between the sides of a right triangle?
Back
In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).
5.
FLASHCARD QUESTION
Front
If the hypotenuse is 10 units and one side is 6 units, how do you find the other side?
Back
Use the Pythagorean Theorem: a² + 6² = 10². Therefore, a² + 36 = 100, so a² = 64, and a = 8 units.
6.
FLASHCARD QUESTION
Front
What is the formula to find the area of a right triangle?
Back
Area = (1/2) * base * height.
7.
FLASHCARD QUESTION
Front
If a right triangle has an area of 24 square units and a base of 8 units, what is the height?
Back
6 units (Using the area formula: 24 = (1/2) * 8 * height, so height = 6).
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