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). It is expressed as: $$a^2 + b^2 = c^2$$ .

The longest side of a right triangle is called the hypotenuse.

Using the Pythagorean Theorem: $$3^2 + 4^2 = c^2$$ , we find that $$c = 5$$ .

In a right triangle, the relationship is defined by the Pythagorean Theorem: $$a^2 + b^2 = c^2$$ .

Yes, because $$5^2 + 12^2 = 13^2$$ (25 + 144 = 169).

A leg is one of the two shorter sides of a right triangle that form the right angle.

Yes, because $$8^2 + 15^2 = 17^2$$ (64 + 225 = 289).

The formula is $$a^2 + b^2 = c^2$$ , where c is the hypotenuse.

Yes, because $$7^2 + 24^2 = 25^2$$ (49 + 576 = 625).

Using the Pythagorean Theorem: $$c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$$ .