Pythagorean Theorem Applications

The video tutorial explains the converse of the Pythagorean theorem, which is used to determine if a triangle is a right triangle by checking if a² + b² = c², where c is the hypotenuse. The tutorial provides three examples: one confirming a right triangle, one disproving it, and one involving square roots. The video concludes by summarizing the method and encouraging viewers to like and subscribe.

What is the main purpose of using the converse of the Pythagorean theorem?

• To calculate the area of a triangle

• To determine if a triangle is a right triangle

• To find the perimeter of a triangle

• To identify the type of angles in a triangle

When applying the converse of the Pythagorean theorem, which side should be identified first?

• The shortest side

• The side opposite the smallest angle

• The hypotenuse, or the longest side

• The side with the largest angle

In the first example, what are the side lengths of the triangle?

• 15, 36, 39

• 12, 35, 37

• 10, 24, 26

• 13, 84, 85

What conclusion is reached in the first example after applying the theorem?

• The triangle is not a right triangle

• The triangle is a right triangle

• The triangle is an equilateral triangle

• The triangle is an isosceles triangle

In the second example, what is the longest side of the triangle?

• 39

• 26

• 33

• 43

What is the result of applying the theorem in the second example?

• The triangle is a right triangle

• The triangle is not a right triangle

• The triangle is an equilateral triangle

• The triangle is an isosceles triangle

In the third example, which side is determined to be the hypotenuse?

• Square root of 130

• Square root of 194

• 18

• Square root of 150

What is the approximate value of the square root of 194 used in the third example?

• 11.4

• 13.9

• 15.2

• 12.7

What is the final conclusion in the third example after applying the theorem?

• The triangle is an isosceles triangle

• The triangle is an equilateral triangle

• The triangle is a right triangle

• The triangle is not a right triangle

What happens when you square a square root, as seen in the third example?

• The square root is halved

• The square root is undone

• The square root is doubled

• The square root is negated