Podcast
Questions and Answers
What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
a squared plus b squared equals c squared
What is the Pythagorean formula for Obtuse Triangles?
What is the Pythagorean formula for Obtuse Triangles?
a squared plus b squared is less than c squared
What is the Pythagorean formula for Acute Triangles?
What is the Pythagorean formula for Acute Triangles?
a squared plus b squared is greater than c squared
In a 30-60-90 triangle, what is the hypotenuse?
In a 30-60-90 triangle, what is the hypotenuse?
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In a 30-60-90 triangle, what is the long leg?
In a 30-60-90 triangle, what is the long leg?
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In a 45-45-90 triangle, what is the hypotenuse?
In a 45-45-90 triangle, what is the hypotenuse?
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In a 45-45-90 triangle, what is the leg?
In a 45-45-90 triangle, what is the leg?
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Study Notes
Pythagorean Theorem
- 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). Formula: ( a^2 + b^2 = c^2 )
Pythagorean Formula for Obtuse Triangles
- For obtuse triangles, the relationship changes, expressed as ( a^2 + b^2 < c^2 ). This indicates that the square of the hypotenuse is greater than the sum of the squares of the other two sides.
Pythagorean Formula for Acute Triangles
- In acute triangles, the condition is that the sum of the squares of the two shorter sides is greater than that of the hypotenuse. This is represented as ( a^2 + b^2 > c^2 ).
30-60-90 Triangle Properties
- In 30-60-90 triangles, the hypotenuse is always double the length of the short leg. Thus, Hypotenuse = short leg × 2.
- The long leg can be calculated as the short leg multiplied by the square root of 3. Therefore, Long leg = short leg × ( \sqrt{3} ).
45-45-90 Triangle Properties
- In 45-45-90 triangles, both legs are equal in length.
- The hypotenuse can be found using the leg length multiplied by the square root of 2. Thus, Hypotenuse = leg × ( \sqrt{2} ).
- To determine the length of a leg using the hypotenuse, apply ( \text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}} ).
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Description
Test your knowledge of the Pythagorean Theorem with these flashcards. Learn about the relationships in right, acute, and obtuse triangles, as well as special triangle properties. Perfect for students studying geometry or preparing for exams.
