Triangle Inequality and Pythagorean Theorem

The video tutorial explains how to determine if a triangle is a right triangle using the converse of the Pythagorean theorem. It begins by ensuring the given sides form a triangle using the triangle inequality theorem. The tutorial then tests if the triangle is right by checking if the square of the longest side equals the sum of the squares of the other two sides. Two examples are provided: one with sides 4, 5, 6, which does not form a right triangle, and another with sides 9, 12, 15, which does form a right triangle.

What is the purpose of testing a triangle using the Pythagorean theorem?

• To determine if it is an equilateral triangle

• To find the area of the triangle

• To calculate the perimeter of the triangle

• To check if it is a right triangle

What does the triangle inequality theorem ensure?

• That the triangle has equal sides

• That the triangle is isosceles

• That the sum of any two sides is greater than the third side

• That the triangle has a right angle

Which sides are used to check the triangle inequality theorem for sides 4, 5, and 6?

• 4 + 5, 5 + 6, 4 + 6

• 4 + 6, 5 + 4, 6 + 5

• 4 + 4, 5 + 5, 6 + 6

• 4 + 5, 5 + 4, 6 + 6

In the example with sides 4, 5, and 6, which side is considered the hypotenuse?

• None

• 6

• 5

• 4

What is the result of 4 squared plus 5 squared in the first example?

• 36

• 16

• 25

• 41

Does the triangle with sides 4, 5, and 6 form a right triangle?

• Maybe

• Yes

• No

• Not enough information

In the second example, what are the sides of the triangle?

• 5, 12, 13

• 9, 12, 15

• 6, 8, 10

• 3, 4, 5

What is the sum of 9 squared and 12 squared in the second example?

• 144

• 225

• 225

• 81

Does the triangle with sides 9, 12, and 15 form a right triangle?

• Yes

• No

• Not enough information

• Maybe

What is the key takeaway from the video?

• All triangles are right triangles

• The Pythagorean theorem can be used to test if a triangle is right

• The triangle inequality theorem is not important

• Only equilateral triangles can be right triangles