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Questions and Answers
According to the Pythagorean Theorem, what is the relationship between the sides of a right-angled triangle?
According to the Pythagorean Theorem, what is the relationship between the sides of a right-angled triangle?
- The hypotenuse is always equal to the sum of the other two sides.
- The square of the hypotenuse is equal to the difference of the squares of the other two sides.
- The square of the hypotenuse is equal to the sum of the squares of the other two sides. (correct)
- The sum of the squares of all three sides is equal to the square of the hypotenuse.
To find a shorter side of a right-angled triangle using the Pythagorean Theorem, you would add the squares of the known sides.
To find a shorter side of a right-angled triangle using the Pythagorean Theorem, you would add the squares of the known sides.
False (B)
What is the formula for the Pythagorean Theorem?
What is the formula for the Pythagorean Theorem?
a² + b² = c²
If the calculated hypotenuse is _ than the actual hypotenuse, the triangle is obtuse-angled.
If the calculated hypotenuse is _ than the actual hypotenuse, the triangle is obtuse-angled.
Match the type of triangle with the corresponding relationship between the calculated hypotenuse and the actual hypotenuse.
Match the type of triangle with the corresponding relationship between the calculated hypotenuse and the actual hypotenuse.
Flashcards
Pythagorean Theorem
Pythagorean Theorem
In a right-angled triangle, a² + b² = c², where c is the hypotenuse.
Finding Hypotenuse
Finding Hypotenuse
Add the squares of the two shorter sides and take the square root to find the hypotenuse.
Finding a Shorter Side
Finding a Shorter Side
Subtract the square of the known side from the square of the hypotenuse, then take the square root.
Right-Angled Triangle
Right-Angled Triangle
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Types of Triangles
Types of Triangles
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Study Notes
Pythagoras Theorem
- The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- The theorem can be expressed as: a² + b² = c² where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.
Finding the Hypotenuse
- To find the hypotenuse, add the squares of the two shorter sides and then take the square root of the sum.
- You are adding the squares to find the hypotenuse, as the hypotenuse is the longest side of the triangle.
Finding a Shorter Side
- To find a shorter side, subtract the square of the known shorter side from the square of the hypotenuse and then take the square root of the difference.
- You are subtracting the squares when finding a shorter side, as the hypotenuse is the longest.
Example Calculations:
- 7² + 8² = 113, √113 = 10.63
- 3² + 5² = 34, √34 = 5.83
- 12² - 10² = 44, √44 = 6.63
Applying the Theorem
- The Theorem is used to determine the length of any side of the triangle if the other two sides are known.
- The Pythagorean Theorem only applies to right-angled triangles.
Identifying Types of Triangles
- If the Pythagorean Theorem holds true, then the triangle is a right-angled triangle.
- If the calculated hypotenuse is less than the actual hypotenuse, the triangle is acute-angled.
- If the calculated hypotenuse is more than the actual hypotenuse, the triangle is obtuse-angled.
Example Calculations for Types of Triangles
- 3² + 4² = 25, √25 = 5, Triangle is right-angled (calculated value is equal to actual value)
- 7² + 10² = 149, √149 = 12.2, Triangle is acute-angled (calculated value is less than actual value)
- 8² + 12² = 208, √208 = 14.4, Triangle is obtuse-angled (calculated value is more than actual value)
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