Pythagorean Theorem and Triangle Types

The video tutorial introduces the Pythagorean Theorem, explaining its definition and application in right triangles. It illustrates the theorem with a diagram and examples, including Pythagorean triples. The converse of the theorem is discussed, showing how it can determine if a triangle is right-angled. Extensions of the converse help identify obtuse and acute triangles. The video concludes with examples to reinforce understanding.

What is the Pythagorean Theorem used for?

• Determining the volume of a cube

• Finding the length of the hypotenuse in a right triangle

• Calculating the area of a circle

• Measuring the perimeter of a rectangle

In a right triangle, which side is the hypotenuse?

• The shortest side

• The side adjacent to the right angle

• The side opposite the right angle

• The side opposite the smallest angle

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

• 7

• 8

• 6

• 5

What does a Pythagorean triple consist of?

• Three irrational numbers

• Three fractions

• Three positive integers that satisfy the Pythagorean Theorem

• Three negative integers

Which of the following is a Pythagorean triple?

• 2, 3, 4

• 5, 12, 13

• 6, 8, 10

• 7, 24, 25

What does the converse of the Pythagorean Theorem state?

• If a² + b² = c², then the triangle is right

• If a triangle is right, then a² + b² = c²

• If a triangle is obtuse, then a² + b² > c²

• If a triangle is acute, then a² + b² < c²

How can you determine if a triangle is obtuse using the converse theorem?

• If c² < a² + b²

• If c² = a² + b²

• If c² > a² + b²

• If a² + b² > c²

What type of triangle is it if c² < a² + b²?

• Right triangle

• Obtuse triangle

• Acute triangle

• Scalene triangle

What is the first step in determining if three numbers can form a triangle?

• Check if the sum of the two smallest numbers is greater than the largest number

• Check if the numbers are all even

• Check if the numbers are all positive

• Check if the numbers are all integers

Given the numbers 9, 40, and 41, what type of triangle do they form?

• Right triangle

• Obtuse triangle

• Acute triangle

• Not a triangle