Pythagorean Theorem Worksheets Printable

Pythagoras

These Pythagorean Theorem worksheets are printable and come with corresponding printable answer pages. In mathematics, the Pythagorean theorem is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Test your knowledge with these Pythagorean Theorem Worksheets.

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Printable Pythagorean Theorem Worksheets (PTWS)
PTWS – A
PTWS – A  Answers
PTWS – B
PTWS – B Answers
PTWS – C
PTWS – C Answers
PTWS – D
PTWS – D Answers
PTWS – E
PTWS – E Answers
PTWS – F
PTWS – F Answers
PTWS – G
PTWS – G Answers
PTWS – H
PTWS – H Answers
PTWS – I
PTWS – I Answers
PTWS – J
PTWS – J Answers

The Pythagorean Theorem is a really important idea in math, and it’s named after a Greek mathematician named Pythagoras. It’s all about right triangles, which are triangles with one angle that’s 90 degrees, like the corner of a book.

Here’s what the Pythagorean Theorem says in a simple way:

“In a right triangle, the square of the length of the longest side, called the hypotenuse, is equal to the sum of the squares of the lengths of the other two sides.”

Now, let’s break that down a bit:

1. Right Triangle: This is a special kind of triangle with one 90-degree angle. The other two angles are smaller, and we call them acute angles.
2. Hypotenuse: This is the longest side of the right triangle, and it’s the one opposite to the 90-degree angle.
3. Squares: To find the square of a number, you multiply it by itself. So, if you have a number like 3, its square would be 3 x 3, which is 9.
4. Sum: This means adding things together. So when we say “the sum of the squares,” we’re talking about adding up the squares of the two shorter sides.

In simple terms, the Pythagorean Theorem helps us figure out the length of one side of a right triangle if we know the lengths of the other two sides. It’s like a secret math tool to solve triangle puzzles! Here’s the formula in math language:

c² = a² + b²

Where:

• “c” is the length of the hypotenuse.
• “a” and “b” are the lengths of the other two sides.

So, if you know the lengths of two sides of a right triangle, you can use this formula to find the length of the third side. It’s a cool trick that helps us understand and work with triangles in math!

Pythagoras of Samos, born around 570 BCE, was an ancient Greek philosopher and mathematician whose contributions have had a lasting impact on mathematics, astronomy, and music theory. He is best known for the Pythagorean theorem, a fundamental principle in geometry that states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Pythagoras traveled extensively in his early years, visiting Egypt and Babylon, where he absorbed a variety of philosophical and mathematical ideas. Upon his return to Greece, he settled in the city of Croton in southern Italy, where he founded a religious and philosophical community known as the Pythagorean Brotherhood. This community was characterized by its ascetic lifestyle and its devotion to the study of mathematics and the pursuit of philosophical wisdom.

Pythagoras and his followers believed that numbers were the fundamental reality of the universe and that mathematical relationships could explain all natural phenomena. This belief extended to music, where Pythagoras discovered that musical intervals could be expressed as simple ratios of whole numbers, leading to significant advancements in the understanding of harmony and acoustics.

Despite his achievements, Pythagoras’ life was shrouded in legend, and much of what is known about him comes from the writings of later philosophers. He was also a mystic who believed in the transmigration of souls, the idea that the soul is immortal and undergoes a cycle of rebirths.

Pythagoras’ influence extended beyond his lifetime, shaping the development of Western philosophical and scientific thought. His emphasis on the importance of numbers and his pioneering work in mathematics laid the groundwork for future generations of scientists and mathematicians. He passed away around 495 BCE, but his legacy endures, enshrined in the annals of history.

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