How does the pythagorean inequality theorem prove acute triangles

The video tutorial explains the characteristics of right and acute triangles, focusing on their angles. It highlights that an acute triangle has all angles less than 90 degrees. The tutorial introduces the Pythagorean inequality as a method to determine if a triangle is acute, where the sum of the squares of two sides must be greater than the square of the third side.

What type of angle is necessary for a triangle to be classified as a right triangle?

• Straight angle

• Acute angle

• Obtuse angle

• Right angle

In an acute triangle, what is true about all of its angles?

• At least one angle is 90 degrees

• All angles are exactly 90 degrees

• All angles are less than 90 degrees

• At least one angle is greater than 90 degrees

Which mathematical concept is used to determine if a triangle is acute?

• Law of Cosines

• Pythagorean theorem

• Law of Sines

• Pythagorean inequality

According to the Pythagorean inequality, when is a triangle considered acute?

• a^2 + b^2 > c^2

• a^2 + b^2 < c^2

• a^2 + b^2 = 2c^2

• a^2 + b^2 = c^2

What is the relationship between the sides of a triangle for it to be classified as acute using the Pythagorean inequality?

• The sum of the squares of two sides is twice the square of the third side

• The sum of the squares of two sides is greater than the square of the third side

• The sum of the squares of two sides is less than the square of the third side

• The sum of the squares of two sides is equal to the square of the third side