Exploring 45-45-90 Triangle Relationships

This video tutorial by Mr. Backberg explores the special relationships between the side lengths of a 45-45-90 triangle. The video explains how to calculate the hypotenuse and legs using the properties of isosceles triangles and the square root of two. Through various examples, the tutorial demonstrates how to find missing sides, simplify calculations, and rationalize radicals. The video provides a clear understanding of the geometric principles involved in solving problems related to 45-45-90 triangles.

What type of triangle is being discussed?

• 30-60-90 triangle

• 45-45-90 triangle

• Isosceles triangle

• Equilateral triangle

What is the relationship between the legs in a 45-45-90 triangle?

• The legs are perpendicular

• One leg is twice the length of the other

• The legs are of equal length

• The legs have unequal lengths

What does the term 'isosceles' imply about the triangle?

• All sides are equal

• Two sides are of equal length

• It has a right angle

• It has no equal sides

How do you find the hypotenuse if you know the length of one leg?

• Divide the leg by 2

• Multiply the leg by 2

• Divide the leg by the square root of 2

• Multiply the leg by the square root of 2

If one leg of the triangle is 8, what is the length of the hypotenuse?

• 8 square root of 2

• 4 square root of 2

• 16

• 8

How do you find the length of the legs if you know the hypotenuse?

• Divide the hypotenuse by the square root of 2

• Divide the hypotenuse by 2

• Multiply the hypotenuse by the square root of 2

• Multiply the hypotenuse by 2

If the hypotenuse is 6, what is the length of each leg?

• 3

• 6 square root of 2

• 6

• 3 square root of 2

If the leg of a 45-45-90 triangle is 3 square root of 2, what is the hypotenuse?

• 6

• 9

• 6 square root of 2

• 3

To rationalize the denominator when dividing by the square root of 2, you should multiply the numerator and denominator by:

• 2

• The square root of 2

• The square root of 3

• 1

In a 45-45-90 triangle, if the hypotenuse is given as 6, how do you find the leg length?

• 6 divided by the square root of 2, then rationalize

• 6 multiplied by 2

• 6 multiplied by the square root of 2

• 6 divided by 2