Question

course 3 unit 2 vocabulary
word definition visual
hypotenuse the side the angle in a right triangle.
legs the two of a right triangle that a right angle.
order of operations the set of which are followed when an expression with than operation.
prime factorization when any number is written as the of all is factors.
pythagorean theorem in a right triangle, the sum of the of the lengths of the is equal to the square of the length of the.
pythagorean triples a set of positive (a, b, c) such that a² + b² = c².
real numbers the set of numbers that includes all and numbers.

Explanation:

Step1: Recall geometry terms

In a right - triangle, the hypotenuse is the longest side opposite the right - angle and legs are the sides forming the right - angle.

Step2: Define order of operations

There are standard rules (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) for evaluating multi - operation expressions.

Step3: Explain prime factorization

Composite numbers can be broken down into a product of prime numbers.

Step4: State Pythagorean Theorem

For a right - triangle with leg lengths \(a\) and \(b\) and hypotenuse length \(c\), \(a^{2}+b^{2}=c^{2}\).

Step5: Define Pythagorean triples

They are integer solutions to the Pythagorean equation.

Step6: Recall real numbers

Real numbers consist of both rational (fractions, integers) and irrational (like \(\pi\), \(\sqrt{2}\)) numbers.

Answer:

• hypotenuse: The side opposite the right - angle in a right triangle.
• legs: The two sides of a right triangle that form a right angle.
• order of operations: The set of rules which are followed when evaluating an expression with more than one operation.
• prime factorization: When any composite number is written as the product of all its prime factors.
• Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
• Pythagorean triples: A set of three positive integers (a, b, c) such that \(a^{2}+b^{2}=c^{2}\).
• real numbers: The set of numbers that includes all rational and irrational numbers.