Pythagorean theorem
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the Pythagorean theorem: in any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a^2 + b^2 = c^2). Students learn to find missing side lengths and verify if triangles are right triangles.
Key Concepts
Property If $c$ stands for the length of the hypotenuse of a right triangle, and the lengths of the two legs are represented by $a$ and $b$, then $$a^2 + b^2 = c^2$$.
Examples For a right triangle with legs $a=3$ and $b=4$, we can find the hypotenuse $c$. The formula gives $3^2 + 4^2 = c^2$, so $9 + 16 = 25 = c^2$. Taking the square root, we find $c=5$.
If a right triangle has a hypotenuse $c=13$ and a leg $a=12$, we find the other leg $b$. The formula gives $12^2 + b^2 = 13^2$, so $144 + b^2 = 169$. Subtracting gives $b^2 = 25$, so $b=5$.
Common Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that for any right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (longest side) and a and b are the legs.
How do you find the hypotenuse using the Pythagorean theorem?
Square both legs, add them together, and take the square root. For example, with legs 3 and 4: c = sqrt(3^2 + 4^2) = sqrt(9+16) = sqrt(25) = 5.
How do you find a missing leg of a right triangle?
Rearrange: a = sqrt(c^2 - b^2). Subtract the square of the known leg from the square of the hypotenuse, then take the square root.
How do you verify if a triangle is a right triangle?
Check if a^2 + b^2 = c^2. If the equation holds, the triangle is a right triangle. If not, it is not.
Where is the Pythagorean theorem taught in Grade 6?
The Pythagorean theorem is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.