Exploring Special Right Triangles II

The video tutorial covers the properties and solutions of 45-45-90 triangles, a type of isosceles right triangle. It explains how to use the Pythagorean theorem to find side lengths and introduces shortcuts for solving these triangles. The tutorial also discusses the use of reference triangles and rationalization of denominators. Advanced examples are provided to illustrate compound triangle problems, emphasizing the relationships between the sides of 45-45-90 triangles.

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

• Right

• Scalene

• Isosceles

• Equilateral

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

• Legs are equal to the hypotenuse

• Hypotenuse is twice the length of a leg

• Hypotenuse is the leg length multiplied by the square root of 2

• Legs are half the length of the hypotenuse

How do you find the length of the hypotenuse if one leg is 5 units in a 45-45-90 triangle?

• 5 square root of 2 units

• 10 units

• 5 units

• 25 units

What is the result of rationalizing the denominator of 6 divided by the square root of 2?

• 3

• 3 square root of 2

• 12

• 6 square root of 2

In a compound triangle scenario, how do you approach finding a side length that is not directly given?

• Find the common side first

• Divide all sides by the square root of 2

• Multiply all sides by 2

• Use the Pythagorean theorem

What is the length of the side opposite the 45-degree angle in a 45-45-90 triangle if the hypotenuse is 8 radical 2?

• 8

• 16

• 4

• 8 radical 2

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known to be 14 units?

• 14 units

• 7 units

• 7 radical 2 units

• 14 radical 2 units

What is the length of the hypotenuse in a 45-45-90 triangle if both legs are 3 radical 2 units?

• 6 radical 2 units

• 6 units

• 3 radical 4 units

• 3 units

If one leg of a 45-45-90 triangle measures 4 radical 5 units, what is the length of the hypotenuse?

• 4 units

• 8 units

• 4 radical 10 units

• 8 radical 5 units

In a 45-45-90 triangle, if the leg opposite the 45-degree angle is 7 units, what is the length of the side opposite the 90-degree angle?

• 7 units

• 14 units

• 7 radical 2 units

• 14 radical 2 units