Proof of the Pythagorean Theorem

The formula to use is $a^{2} + b^{2} = c^{2}$. Here, $a = 3$ and $b = 4$. Plugging in the values, we get $3^{2} + 4^{2} = 9 + 16 = 25$. Therefore, $c = \sqrt{25} = 5$.

Using the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$, where $a = 6$ and $b = 8$, we have $6^{2} + 8^{2} = 36 + 64 = 100$. Therefore, $c = \sqrt{100} = 10$ units.

Applying the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$, where $a = 5$ and $b = 12$, we calculate $5^{2} + 12^{2} = 25 + 144 = 169$. Hence, $c = \sqrt{169} = 13$ units.

Using the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$, where $a = 9$ and $b = 12$, we find $9^{2} + 12^{2} = 81 + 144 = 225$. Therefore, $c = \sqrt{225} = 15$ units.

By applying the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$, where $a = 7$ and $b = 24$, we obtain $7^{2} + 24^{2} = 49 + 576 = 625$. Thus, $c = \sqrt{625} = 25$ units.

Using the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$, where $a = 8$ and $b = 15$, we calculate $8^{2} + 15^{2} = 64 + 225 = 289$. Hence, $c = \sqrt{289} = 17$ units.

The Pythagorean Theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, although evidence suggests that it was known to earlier civilizations as well.

No, the Pythagorean Theorem only applies to right triangles.

The Pythagorean Theorem is important because it provides a method to determine the length of a side of a right triangle, which is useful in various real-world applications, including construction, navigation, and engineering.

No, there are numerous proofs of the Pythagorean Theorem, each illustrating the theorem in a unique way.

Pythagorean triples are sets of three integers that fit the Pythagorean equation, such as (3, 4, 5) and (5, 12, 13).

Yes, visualisation usually involves a right triangle with squares constructed on each side to represent the theorem geometrically.

Yes, the Pythagorean Theorem is used in various fields such as physics, engineering, and computer graphics.

Yes, there are generalisations of the Pythagorean Theorem for higher dimensions, known as the Pythagorean theorem in n dimensions. Once you get confident with the Pythagorean Theorem in 2D, you can start to look at it in 3D shapes!

Yes, one famous anecdote involves the discovery of irrational numbers by Pythagoras' followers while attempting to calculate the length of the diagonal of a square.