Pythagorean Theorem and Triangle Types

This video tutorial covers the Pythagorean theorem and its converse to determine if a triangle is acute, right, or obtuse. It also discusses the triangle inequality, which is essential for determining if a triangle can be formed with given side lengths. The video provides examples to illustrate these concepts, showing how to apply the Pythagorean theorem and triangle inequality to classify triangles. The tutorial concludes with a summary of the key points discussed.

What does the Pythagorean Theorem state?

• a^2 + b^2 = 2c^2

• a^2 + b^2 = c^2

• a^2 + b^2 < c^2

• a^2 + b^2 > c^2

If c^2 is less than a^2 + b^2, what type of triangle is it?

• Right triangle

• Acute triangle

• Obtuse triangle

• Scalene triangle

What must be true for three segments to form a triangle?

• The sum of the two shorter sides must be twice the longest side.

• The sum of the two shorter sides must be equal to the longest side.

• The sum of the two shorter sides must be less than the longest side.

• The sum of the two shorter sides must be greater than the longest side.

In Example 1, what type of triangle is formed with sides 7, 24, and 25?

• Acute triangle

• Right triangle

• Obtuse triangle

• No triangle

In Example 1, what is the value of 25 squared?

• 144

• 625

• 49

• 576

In Example 2, what type of triangle is formed with sides 5, 12, and 16?

• Obtuse triangle

• No triangle

• Right triangle

• Acute triangle

In Example 2, what is the sum of 5 squared and 12 squared?

• 144

• 25

• 169

• 256

In Example 3, what type of triangle is formed with sides 6, 8, and 9?

• No triangle

• Obtuse triangle

• Right triangle

• Acute triangle

In Example 3, what is the value of 9 squared?

• 64

• 36

• 81

• 100

In Example 4, why is it not possible to form a triangle with sides 3, 5, and 9?

• Because 3 + 5 is not greater than 9

• Because 3 + 5 is less than 9

• Because 3 + 5 is greater than 9

• Because 3 + 5 is equal to 9