Questions: 2. Who is the Pythagorean Theorem named after? a. Euclid b. Aristotle c. Pythagoras d. Archimedes 3. Which side of a right triangle is the longest? a. The leg b. The hypotenuse c. The base d. The height 4. In the equation ( a^2+b^2=c^2 ), what does (c) represent? a. The length of one leg b. The length of the hypotenuse c. The perimeter of the triangle d. The area of the triangle

2. Who is the Pythagorean Theorem named after? a. Euclid b. Aristotle c. Pythagoras d. Archimedes 3. Which side of a right triangle is the longest? a. The leg b. The hypotenuse c. The base d. The height 4. In the equation ( a^2+b^2=c^2 ), what does (c) represent? a. The length of one leg b. The length of the hypotenuse c. The perimeter of the triangle d. The area of the triangle
Transcript text: 2. Who is the Pythagorean Theorem named after? a. Euclid b. Aristotle c. Pythagoras d. Archimedes 3. Which side of a right triangle is the longest? a. The leg b. The hypotenuse c. The base d. The height 4. In the equation ( $a^{\wedge} 2+b^{\wedge} 2=c^{\wedge} 2$ ), what does (c) represent? a. The length of one leg b. The length of the hypotenuse c. The perimeter of the triangle d. The area of the triangle
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Solution

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Solution Steps

Solution Approach
  1. The Pythagorean Theorem is named after Pythagoras.
  2. The longest side of a right triangle is the hypotenuse.
  3. In the equation \(a^2 + b^2 = c^2\), \(c\) represents the length of the hypotenuse.
Step 1: Pythagorean Theorem Origin

The Pythagorean Theorem is named after the ancient Greek mathematician \( Pythagoras \).

Step 2: Longest Side of a Right Triangle

In a right triangle, the longest side is known as the \( \text{hypotenuse} \).

Step 3: Meaning of \( c \) in the Pythagorean Theorem

In the equation \( a^2 + b^2 = c^2 \), the variable \( c \) represents the length of the \( \text{hypotenuse} \).

Final Answer

The answers to the questions are:

  1. The Pythagorean Theorem is named after: \( \boxed{\text{Pythagoras}} \)
  2. The longest side of a right triangle is: \( \boxed{\text{hypotenuse}} \)
  3. In the equation \( a^2 + b^2 = c^2 \), \( c \) represents: \( \boxed{\text{length of the hypotenuse}} \)
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