Example Card: Verifying a Pythagorean Triple
Master Verifying a Pythagorean Triple for Grade 9 math with step-by-step practice. Can any three numbers form a right triangle?
Key Concepts
Can any three numbers form a right triangle? Let's use the theorem in reverse to find out. This example uses the second key idea: the Converse of the Pythagorean Theorem.
Example Problem Determine whether the side lengths 7, 24, and 25 form a Pythagorean triple.
Step by Step 1. To check if the side lengths form a right triangle, we see if they satisfy the equation $a^2 + b^2 = c^2$. Remember to substitute the greatest number for $c$. $$7^2 + 24^2 \stackrel{?}{=} 25^2$$ 2. Calculate the squares of each number. $$49 + 576 \stackrel{?}{=} 625$$ 3. Add the values on the left side of the equation. $$625 = 625$$ 4. The equation is true. Because 7, 24, and 25 are three nonzero whole numbers that satisfy the Pythagorean theorem, they form a Pythagorean triple.
Common Questions
What is Verifying a Pythagorean Triple in Algebra 1?
Verifying a Pythagorean Triple is a core Grade 9 Algebra 1 concept covering properties and applications.
How do you work with Verifying a Pythagorean Triple in Grade 9 math?
A Pythagorean triple is like a VIP pass for right triangles. It's a special set of three positive whole numbers (, , and ) that perfectly fit the Pythagorean theorem, . Think of it as a perfect triangle team with no decimals or fractions allowed! To check if a set of numbers is a Pythagorean triple,.
What are common mistakes when learning Verifying a Pythagorean Triple?
A Pythagorean triple is like a VIP pass for right triangles. It's a special set of three positive whole numbers (, , and ) that perfectly fit the Pythagorean theorem, . Think of it as a perfect triangle team with no decimals or fractions allowed! To check if a set of numbers is a Pythagorean triple, you must verify two rules: 1. The Whole Number Ru.