Pythagorean Theorem and Triangle Types

The video tutorial explains the Pythagorean Theorem and its converse, which is used to determine if a triangle is a right triangle. It further explores the Pythagorean Inequality Theorem, which helps classify triangles as acute or obtuse based on the relationship between the sum of the squares of the legs and the hypotenuse. The tutorial concludes with a brief explanation of inequality symbols.

What is the primary use of the Pythagorean Inequality Theorem?

• To calculate the area of a triangle

• To measure the angles of a triangle

• To find the perimeter of a triangle

• To determine the type of triangle

What does the converse of the Pythagorean Theorem help determine?

• If a triangle is scalene

• If a triangle is a right triangle

• If a triangle is isosceles

• If a triangle is equilateral

If the sum of the squares of the legs equals the square of the hypotenuse, what type of triangle is it?

• Scalene

• Right

• Obtuse

• Acute

What is the hypotenuse in a right triangle?

• The shortest side

• Any side

• The longest side

• The side opposite the smallest angle

If given three sides of a triangle, how can you determine if it is a right triangle?

• Check if the sum of the squares of the two longer sides equals the square of the shortest side

• Check if the sum of the squares of the two shorter sides equals the square of the longest side

• Check if the sum of the squares of the two shorter sides is less than the square of the longest side

• Check if the sum of the squares of all three sides equals zero

What type of triangle is it if the sum of the squares of the legs is greater than the square of the hypotenuse?

• Right

• Obtuse

• Equilateral

• Acute

What type of triangle is it if the sum of the squares of the legs is less than the square of the hypotenuse?

• Right

• Acute

• Obtuse

• Isosceles

Which symbol represents 'less than'?

• ≥

• =

• <

• >

Which symbol represents 'greater than'?

• <

• >

• ≤

• =

What does the Pythagorean Inequality Theorem help classify?

• The type of angles in a triangle

• The type of triangle based on side lengths

• The perimeter of a triangle

• The area of a triangle