Pythagorean theorem
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². Taught in Yoshiwara Elementary Algebra Chapter 5: Exponents and Roots, this theorem is a fundamental tool for Grade 6 students to find missing side lengths in right triangles. It connects algebra with geometry and has wide applications in distance, construction, and coordinate geometry.
Key Concepts
Property A right triangle contains a 90° angle. The side opposite the right angle is the hypotenuse ($c$), and the other two sides are the legs ($a$ and $b$).
The Pythagorean Theorem states that for any right triangle:.
$$a^2 + b^2 = c^2$$.
Common Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a and b are the two legs.
How do you find the hypotenuse using the Pythagorean theorem?
Square both legs, add them, and take the square root: c = √(a² + b²). For example, with legs 3 and 4, the hypotenuse is √(9 + 16) = √25 = 5.
How do you find a missing leg using the Pythagorean theorem?
Rearrange the formula: a² = c² - b², then take the square root of both sides to find a.
Where is the Pythagorean theorem in Yoshiwara Elementary Algebra?
It is covered in Chapter 5: Exponents and Roots of Yoshiwara Elementary Algebra.
What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², like 3-4-5 or 5-12-13.