Pythagorean theorem: find the length of the hypotenuse (Introduction)

Learning Objectives Identify the hypotenuse and legs of a right-angled triangle. State the Pythagorean theorem formula. Calculate the square of a given whole number. Substitute known leg lengths into the Pythagorean theorem equation. Calculate the square root of perfect squares. Find the length of the hypotenuse of a right-angled triangle using the Pythagorean theorem. Ever wondered how construction workers make sure walls are perfectly straight, or how you can find the shortest distance across a field without walking it? 🤔 In this lesson, you'll discover a powerful mathematical rule called the Pythagorean theorem. You'll learn how to use it to find the length of the longest side of a special type of triangle, which is super useful for solving real-world problems...

TermDefinitionExample Right-angled triangleA triangle that has one angle measuring exactly 90 degrees (a right angle).A triangle with sides 3 cm, 4 cm, and 5 cm is a right-angled triangle. Right angleAn angle that measures exactly 90 degrees, often marked with a small square symbol in the corner.The corner of a square or a book forms a right angle. HypotenuseThe longest side of a right-angled triangle, always located directly opposite the right angle.In a right triangle with sides 5, 12, and 13, the side with length 13 is the hypotenuse. LegsThe two shorter sides of a right-angled triangle that form the right angle.In a right triangle with sides 5, 12, and 13, the sides with lengths 5 and 12 are the legs. Square of a numberThe result of multiplying a number by itself (e.g., $x^2 = x \time...

Pythagorean Theorem $a^2 + b^2 = c^2$ In a right-angled triangle, the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the lengths of the two legs ($a$ and $b$). This rule only applies to right triangles. Squaring a Number $x^2 = x \times x$ To find the square of any number, multiply the number by itself. This is a fundamental operation in the Pythagorean theorem. Finding the Hypotenuse $c = \sqrt{a^2 + b^2}$ After finding the sum of the squares of the legs ($a^2 + b^2$), take the square root of that sum to find the actual length of the hypotenuse ($c$). This is the final step in calculating 'c'.