Exploring the Converse of the Pythagorean Theorem

What does the Pythagorean theorem state about a right triangle?

• The square of the hypotenuse equals the sum of the squares of the other two sides.

• The sum of the angles equals 180 degrees.

• The area of the triangle can be found using base times height.

• The length of the hypotenuse is twice the length of the shortest side.

What is the purpose of squaring the sides in the Pythagorean theorem?

• To find the area of the triangle.

• To eliminate negative values.

• To comply with the theorem's formula.

• To calculate the perimeter of the triangle.

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

• By checking if the sum of the angles equals 180 degrees.

• By confirming if the square of the longest side equals the sum of the squares of the other two sides.

• By comparing it to a known right triangle.

• By measuring each side with a ruler.

What is the first step in using the converse of the Pythagorean theorem to verify a right triangle?

• Square the lengths of all sides.

• Identify the longest side as the hypotenuse.

• Add the lengths of the two shorter sides.

• Draw the triangle on a graph.

Why is it important to identify the longest side when using the Pythagorean theorem?

• It determines the height of the triangle.

• It is considered the hypotenuse in a right triangle.

• It helps in calculating the area of the triangle.

• It is always the base of the triangle.

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

• Multiply the lengths of the known sides.

• Add the lengths of the known sides.

• Subtract the length of one known side from the other.

• Use the Pythagorean theorem to solve for the unknown side.

How is the distance formula derived from the Pythagorean theorem?

• By multiplying the x-coordinate difference with the y-coordinate difference.

• By finding the average of the x and y coordinates.

• By adding the x and y coordinates directly.

• By squaring the difference in x-coordinates and adding it to the square of the difference in y-coordinates.

What does the distance formula calculate?

• The difference in the x-coordinates of two points.

• The length of the hypotenuse in a right triangle formed by two points.

• The area of a triangle.

• The perimeter of a triangle.

What does the distance formula help to determine?

• The shortest path between two points in a plane.

• The midpoint between two points.

• The slope of the line connecting two points.

• The angle between two lines.

Why might the distance formula be preferred over direct measurement for finding distances on a coordinate plane?

• It is more accurate than using a ruler.

• It can be used without a graph.

• It provides an exact value rather than an estimate.

• It is easier to calculate.