Explore the foundational concepts of mathematics, including algebra, geometry, and data analysis, essential for 8th-grade students.
The Pythagorean Theorem is a special rule about right triangles (triangles with a 90-degree angle). It tells us how the lengths of the sides are related. If you know two sides, you can always find the third!
The sides that form the right angle are called legs (\( a \) and \( b \)), and the longest side is the hypotenuse (\( c \)). The theorem says:
\[ a^2 + b^2 = c^2 \]
This is super useful for measuring distances you can't reach directly. Architects, engineers, and even video game designers use the Pythagorean Theorem to build things and solve problems.
\[a^2 + b^2 = c^2\]
A ladder is 10 feet away from a wall and reaches up 24 feet. The length of the ladder is \( \sqrt{10^2 + 24^2} = 26 \) feet.
If a rectangular playground is 30 meters long and 40 meters wide, the diagonal across it is \( \sqrt{30^2 + 40^2} = 50 \) meters.
The Pythagorean Theorem connects the sides of right triangles to help us measure distances.