Introduction to the Pythagorean theorem | Right triangles and trigonometry | Geometry | Khan Academy

TL;DR

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

Transcript

Welcome to the presentation on the Pythagorean theorem. I apologize if my voice sounds a little horsie. A little hoarse, not horsie. I was singing a little bit too much last night, so please forgive me. Well, anyway, we will now teach you about the Pythagorean theorem. And you might have heard of this before. As far as I know, it is the only mathem... Read More

Key Insights

• 😖 The Pythagorean theorem is named after Pythagoras, who founded a religion based on mathematics.
• 🗯️ The hypotenuse of a right triangle is the side opposite the right angle and is the longest side.
• 🈸 The Pythagorean theorem is a powerful formula that has applications in Euclidean geometry and trigonometry.
• 🙃 The theorem can be used to find the length of an unknown side in a right triangle when the lengths of the other two sides are known.
• 🗯️ The Pythagorean theorem is based on the relationship between the areas of squares built on each side of a right triangle.
• ❎ The formula A squared plus B squared equals C squared is a concise representation of the Pythagorean theorem.
• 👍 The Pythagorean theorem can be proven geometrically or through a visual proof.

Questions & Answers

Q: What is the Pythagorean theorem?

The Pythagorean theorem is a mathematical formula that relates the lengths of the sides in a right triangle. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Q: Why is the hypotenuse the longest side in a right triangle?

The hypotenuse is the longest side in a right triangle because it is opposite the 90-degree angle, which is the largest angle in the triangle.

Q: How can we use the Pythagorean theorem to find the length of a side in a right triangle?

By knowing the lengths of two sides in a right triangle, we can use the Pythagorean theorem to find the length of the third side. We square the lengths of the known sides, add them together, and then take the square root to find the length of the unknown side.

Q: Can the Pythagorean theorem be applied to all triangles?

No, the Pythagorean theorem only applies to right triangles, which have one 90-degree angle. Other types of triangles, such as acute or obtuse triangles, do not satisfy the conditions of the theorem.

Summary & Key Takeaways

• The Pythagorean theorem is a mathematical theorem named after Pythagoras and is used to calculate the length of the third side in a right triangle.

• A right triangle has one side equal to 90 degrees, and the side opposite the right angle is called the hypotenuse.

• The Pythagorean theorem states that A squared plus B squared is equal to C squared, where C is the length of the hypotenuse.