Exploring the Pythagorean Theorem and Distance Concepts

What is the longest side of a right triangle called?

• Leg

• Altitude

• Base

• Hypotenuse

In the Pythagorean Theorem, what do 'a' and 'b' represent?

• The hypotenuse

• The area of the triangle

• The two short sides

• The angles

If one leg of a right triangle is 4 and the hypotenuse is 9, what is the length of the other leg?

• √65

• 7

• 8

• 5

Why do we only consider the positive square root when using the Pythagorean Theorem?

• Because it is easier to calculate

• Because side lengths cannot be negative

• Because it is a rule of geometry

• Because it simplifies the equation

How can the Pythagorean Theorem be used to verify if a triangle is a right triangle?

• By measuring the angles directly

• By plugging in the side lengths and checking if the equation holds true

• By ensuring the longest side is opposite the right angle

• By checking if the sum of the angles is 180 degrees

Given a triangle with legs of 3 and 4, what is the length of the hypotenuse?

• 7

• 5

• 6

• 8

What is the Distance Formula used for?

• Determining the slope of a line

• Calculating the area of a triangle

• Finding the distance between two points

• Finding the midpoint between two points

Which of the following is the correct Distance Formula?

• √((x1 + x2)² + (y1 + y2)²)

• √((x1 - x2)² + (y1 - y2)²)

• √((x1 * x2)² + (y1 * y2)²)

• √((x1 / x2)² + (y1 / y2)²)

What does the Midpoint Formula calculate?

• The distance between two points

• The slope of a line

• The area of a triangle

• The midpoint between two points

How is the midpoint between two points (x1, y1) and (x2, y2) found?

• ((x1 / x2) / 2, (y1 / y2) / 2)

• ((x1 * x2) / 2, (y1 * y2) / 2)

• ((x1 - x2) / 2, (y1 - y2) / 2)

• ((x1 + x2) / 2, (y1 + y2) / 2)