Understanding Triangle Types with the Pythagorean Theorem

Mr. Rey explains the Pythagorean Theorem and explores what happens when a² + b² ≠ c². He discusses how this applies to non-right triangles, specifically obtuse and acute triangles, and provides examples to classify triangles based on side lengths. The video demonstrates how the theorem can be used beyond right triangles to determine the type of triangle based on side lengths.

What does the Pythagorean Theorem traditionally state about the sides of a right triangle?

• The sum of the squares of the two shorter sides equals the square of the longest side.

• The square of the longest side is less than the sum of the squares of the other two sides.

• The sum of the squares of the two longer sides equals the square of the shortest side.

• The sum of the squares of all three sides equals zero.

What happens to the angle of a triangle if the longest side is too long to be a hypotenuse?

• The angle becomes a right angle.

• The angle becomes an obtuse angle.

• The angle becomes an acute angle.

• The angle remains unchanged.

If the largest side of a triangle is too small, what type of triangle is formed?

• Obtuse triangle

• Right triangle

• Acute triangle

• Equilateral triangle

How can the Pythagorean Theorem be used beyond finding a missing side in a right triangle?

• To determine the area of a triangle

• To calculate the angles of a triangle

• To classify a triangle as acute, obtuse, or right

• To find the perimeter of a triangle

In the example with sides 6, 8, and 9, what type of triangle is formed?

• Right triangle

• Scalene triangle

• Obtuse triangle

• Acute triangle

For a triangle with sides 6, 8, and 11, what is the classification?

• Acute triangle

• Obtuse triangle

• Right triangle

• Isosceles triangle

What is the classification of a triangle with sides 5, 12, and 10?

• Right triangle

• Obtuse triangle

• Equilateral triangle

• Acute triangle

What type of triangle is formed with sides 5, 12, and 13?

• Right triangle

• Obtuse triangle

• Acute triangle

• Isosceles triangle

In the example with sides 5, 12, and 15, what type of triangle is formed?

• Obtuse triangle

• Acute triangle

• Right triangle

• Scalene triangle

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

• It determines the perimeter of the triangle.

• It is always the hypotenuse.

• It helps classify the triangle as acute, obtuse, or right.

• It is irrelevant to the triangle's classification.