Pythagorean Theorem
A triangle in which one of the angles is a right angle, or 90^\circ, is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs. If c stands for the length of the hypotenuse, and the lengths of the two legs are a and b, then: a^2 + b^2 = c^2 In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. This skill is part of Grade 8 math in Yoshiwara Core Math.
Key Concepts
Property A triangle in which one of the angles is a right angle, or $90^\circ$, is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs.
If $c$ stands for the length of the hypotenuse, and the lengths of the two legs are $a$ and $b$, then: $$a^2 + b^2 = c^2$$ In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Examples A right triangle has legs of length 3 cm and 4 cm. To find the hypotenuse $c$, we use $3^2 + 4^2 = c^2$. This gives $9 + 16 = 25$, so $c^2=25$, and the hypotenuse is 5 cm.
Common Questions
What is Pythagorean Theorem?
A triangle in which one of the angles is a right angle, or 90^\circ, is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse.
How does Pythagorean Theorem work?
Example: A right triangle has legs of length 3 cm and 4 cm. To find the hypotenuse c, we use 3^2 + 4^2 = c^2. This gives 9 + 16 = 25, so c^2=25, and the hypotenuse is 5 cm.
Give an example of Pythagorean Theorem.
Do side lengths 8, 15, and 17 form a right triangle? Check: 8^2 + 15^2 = 64 + 225 = 289. Since 17^2 = 289, the sides form a right triangle.
Why is Pythagorean Theorem important in math?
This famous theorem is a special property of right triangles. It creates a relationship between the three sides.
What grade level covers Pythagorean Theorem?
Pythagorean Theorem is a Grade 8 math topic covered in Yoshiwara Core Math in Chapter 3: Measurement. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.
What are the key rules for Pythagorean Theorem?
The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs. If c stands for the length of the hypotenuse, and the lengths of the two legs are a and b, then: a^2 + b^2 = c^2 In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse..
What are typical Pythagorean Theorem problems?
A right triangle has legs of length 3 cm and 4 cm. To find the hypotenuse c, we use 3^2 + 4^2 = c^2. This gives 9 + 16 = 25, so c^2=25, and the hypotenuse is 5 cm.; Do side lengths 8, 15, and 17 form a right triangle? Check: 8^2 + 15^2 = 64 + 225 = 289. Since 17^2 = 289, the sides form a right triangle.; A right triangle has a hypotenuse of 13 and one leg of 5. To find the other leg b, we solve 5^2 + b^2 = 13^2. This is 25 + b^2 = 169. So, b^2 =