Understanding 45-45-90 Triangles

This video tutorial explains the properties and special rules of 45-45-90 triangles, which are isosceles right triangles. It covers how to solve these triangles using known side lengths and the special ratio involving the square root of two. The tutorial includes examples of both forward and backward problems, demonstrating how to calculate unknown sides using these rules.

What type of triangle is a 45-45-90 triangle?

• Obtuse

• Scalene

• Equilateral

• Isosceles

In a 45-45-90 triangle, what is the relationship between the two legs?

• One leg is half the other

• The legs are equal

• One leg is twice the other

• The legs are unrelated

In a 45-45-90 triangle, if one leg is known, how can you find the hypotenuse?

• Multiply the leg by the square root of 2

• Divide the leg by 2

• Multiply the leg by 3

• Add 5 to the leg

If one leg of a 45-45-90 triangle is 7, what is the length of the hypotenuse?

• 7√3

• 7√2

• 14

• 7

What is the first step in solving a backward problem when the hypotenuse is known?

• Multiply by the square root of 3

• Subtract the square root of 3

• Divide by the square root of 2

• Add the square root of 2

Why do we rationalize the denominator when solving backward problems?

• To make the fraction easier to read

• To increase the value of the fraction

• To decrease the value of the fraction

• To eliminate the radical from the denominator

What is the simplified form of 12 divided by the square root of 2?

• 6√2

• 12√2

• 6

• 12

What is the result of multiplying the square root of 2 by itself?

• 4

• 3

• 2

• 1

What is the purpose of using the square root of 2 in 45-45-90 triangles?

• To find the area

• To find the perimeter

• To calculate the hypotenuse

• To determine the angles

What is the key takeaway from solving forward and backward problems in 45-45-90 triangles?

• The angles are always 60 degrees

• The legs are always shorter

• The hypotenuse is always longer

• The square root of 2 is crucial for calculations