Exploring the Pythagorean Theorem through Examples

The video tutorial explains the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. The video demonstrates how to apply this theorem to solve for missing sides in right triangles through three examples. The first example solves for a missing leg, the second for the hypotenuse, and the third involves an isosceles right triangle.

What does the Pythagorean theorem state about the relationship between the sides of a right triangle?

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

• The square of each leg equals the square of the hypotenuse divided by two.

• The sum of the squares of the hypotenuse equals twice the square of one leg.

• The sum of the lengths of the two legs equals the length of the hypotenuse.

What is the correct expression for the Pythagorean theorem?

• a^2 + b^2 = c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = 2c^2

• 2a^2 = b^2 + c^2

In a right triangle with legs of lengths 4 and an unknown, and a hypotenuse of 5, what is the length of the unknown leg?

• 4

• 6

• 5

• 3

If the hypotenuse is 5 and one leg is 4, what is the length of the other leg in a right triangle?

• 3

• 1

• 2

• 2.5

How do you determine the length of the hypotenuse if the lengths of the legs are 9 and 7?

• Square root of 145

• Square root of 112

• Square root of 130

• Square root of 81

What is the simplified form of the square root of 130?

• Square root of 130

• 10 square root of 13

• 2 square root of 65

• 13 square root of 10

What is the result of 9 squared plus 7 squared?

• 136

• 126

• 130

• 145

In a right triangle, if one leg is 4 and the hypotenuse is 4 square roots of 2, what is the length of the other leg?

• 2

• 8

• 4

• 16

What type of triangle is formed if both legs are equal and the hypotenuse is 4 times the square root of 2?

• Acute triangle

• Scalene triangle

• Isosceles right triangle

• Equilateral triangle

If a right triangle has a hypotenuse of 4 square roots of 2 and one leg of 4, what is the length of the other leg?

• 16

• 2

• 8

• 4