Understanding the Pythagorean Theorem and Its Applications

What is the condition for a triangle to be classified as a right triangle using 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 side lengths 9, 12, and 15, why is the triangle classified as a right triangle?

• Because 9^2 - 12^2 = 15^2

• Because 9^2 + 12^2 > 15^2

• Because 9^2 + 12^2 = 15^2

• Because 9^2 + 12^2 < 15^2

How do you determine the hypotenuse in a triangle when using the Pythagorean theorem?

• It is the side opposite the largest angle

• It is the side opposite the smallest angle

• It is the longest side

• It is the shortest side

What does it mean if a^2 + b^2 is greater than c^2 in a triangle?

• The triangle is right

• The triangle is acute

• The triangle is equilateral

• The triangle is obtuse

In the example with side lengths 9.6, 18, and 20.1, what type of triangle is it?

• Scalene triangle

• Acute triangle

• Right triangle

• Obtuse triangle

What is the significance of the largest side in determining the type of triangle using the Pythagorean theorem?

• It is always the base

• It is always the median

• It is always the height

• It is always the hypotenuse

In the example with side lengths 6, 2√55, and 17, why is the triangle classified as obtuse?

• Because 6^2 - (2√55)^2 = 17^2

• Because 6^2 + (2√55)^2 < 17^2

• Because 6^2 + (2√55)^2 > 17^2

• Because 6^2 + (2√55)^2 = 17^2

What is the result of 28.6^2 + 4.8^2 in the context of the Pythagorean theorem?

• Equal to 28.6^2

• Equal to 29^2

• Greater than 29^2

• Less than 29^2

How can you classify a triangle if a^2 + b^2 is less than c^2?

• Isosceles triangle

• Right triangle

• Acute triangle

• Obtuse triangle

In the context of the Pythagorean theorem, what does it mean if a^2 + b^2 equals c^2?

• The triangle is right

• The triangle is acute

• The triangle is scalene

• The triangle is obtuse