Triangle Types and Pythagorean Theorem

The video tutorial from Friendly Math 101 covers Pythagorean inequalities, explaining how to determine if a triangle is right, acute, or obtuse based on the relationship between the squares of its sides. The lesson includes three examples: an acute triangle where the sum of the squares of the two shorter sides is greater than the square of the longest side, a right triangle where these sums are equal, and an obtuse triangle where the sum of the squares of the two shorter sides is less than the square of the longest side. The tutorial concludes with a prompt to subscribe for more math lessons.

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

• a squared divided by b squared equals c squared

• a squared minus b squared equals c squared

• a squared plus b squared equals c squared

• a squared times b squared equals c squared

What is the longest side of a triangle called?

• Median

• Hypotenuse

• Height

• Base

What is the sum of the squares of the two shorter sides in a right triangle equal to?

• The square of the hypotenuse

• The product of the hypotenuse

• The sum of the hypotenuse

• The difference of the hypotenuse

If a squared plus b squared is greater than c squared, what type of triangle is it?

• Equilateral triangle

• Obtuse triangle

• Acute triangle

• Right triangle

What type of triangle is formed when a squared plus b squared equals c squared?

• Scalene triangle

• Acute triangle

• Right triangle

• Obtuse triangle

Which inequality indicates an obtuse triangle?

• a squared plus b squared is less than c squared

• a squared plus b squared is greater than c squared

• a squared plus b squared equals c squared

• a squared plus b squared is not equal to c squared

In the context of triangles, what does the term 'acute' refer to?

• All angles are 90 degrees

• All angles are equal

• All angles are less than 90 degrees

• All angles are more than 90 degrees

In the first example, what is the relationship between 12 squared plus 10 squared and 15 squared?

• Greater than

• Not comparable

• Equal to

• Less than

What conclusion is drawn from the first example when 12 squared plus 10 squared is greater than 15 squared?

• The triangle is right

• The triangle is acute

• The triangle is equilateral

• The triangle is obtuse

What is the result of 15 squared in the first example?

• 729

• 244

• 225

• 289