Pythagorean Theorem Applications

The video tutorial explains how to determine if a set of three sides forms a right triangle using the Pythagorean theorem. It provides three examples: two that confirm right triangles and one that does not. The first example uses whole numbers, the second involves radical numbers, and the third shows a non-right triangle. The tutorial emphasizes the importance of verifying the equation a² + b² = c² to confirm a right triangle.

What is the condition for a triangle to be classified as a right triangle?

• a^2 + b^2 < c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

• a^2 + b^2 > c^2

Which of the following is a correct application of the Pythagorean theorem?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 < c^2

• a^2 + b^2 > c^2

In the example with sides a = 12, b = 9, and c = 15, what is the value of a^2 + b^2?

• 144

• 225

• 81

• 225

For the triangle with sides a = 12, b = 9, and c = 15, what is the value of c^2?

• 196

• 81

• 225

• 144

In the example with a = 12, b = 9, and c = 15, what is the sum of a^2 and b^2?

• 225

• 144

• 81

• 196

In the example with a = 10, b = 2√39, and c = 16, what is the value of b^2?

• 156

• 100

• 256

• 196

What is the value of c^2 in the example with a = 10, b = 2√39, and c = 16?

• 196

• 156

• 256

• 100

What is the value of a^2 in the example with a = 10, b = 2√39, and c = 16?

• 196

• 156

• 256

• 100

In the example with a = 10, b = 2√39, and c = 16, what is the sum of a^2 and b^2?

• 196

• 100

• 256

• 156

In the example with a = 9, b = √115, and c = 11, what is the value of a^2?

• 115

• 196

• 81

• 121