Properties of 45-45-90 Triangles

The video tutorial explains how to solve 45-45-90 triangles, a special type of right triangle. It begins by describing the properties and ratios of the sides of these triangles. The tutorial then provides two examples: one where the length of a leg is known and another where the hypotenuse is known. In each case, the method involves using the known side to find the value of X, which is then used to determine the lengths of the other sides. The key takeaway is understanding the consistent ratios in 45-45-90 triangles and applying them to solve for unknown side lengths.

What is another name for a 45-45-90 triangle?

• Equilateral triangle

• Isosceles right triangle

• Scalene triangle

• Acute triangle

In a 45-45-90 triangle, if one leg is labeled as 1, what is the length of the hypotenuse?

• 2

• Square root of 2

• Square root of 3

• 1

What remains constant in all 45-45-90 triangles?

• The ratios of the lengths of the sides

• The area of the triangle

• The lengths of the sides

• The perimeter of the triangle

If each side of a 45-45-90 triangle is multiplied by X, what is the length of the hypotenuse?

• X

• X divided by 2

• X squared

• X times square root of 2

In a 45-45-90 triangle, if one leg is 12 feet, what is the length of the other leg?

• 12 square root of 2 feet

• 12 feet

• 6 feet

• 24 feet

Given one leg of a 45-45-90 triangle is 12 feet, what is the length of the hypotenuse?

• 6 square root of 2 feet

• 24 feet

• 12 square root of 2 feet

• 12 feet

In a 45-45-90 triangle, if the hypotenuse is 9 cm, what is the length of each leg?

• 9 square root of 2 cm

• 9 cm

• 9 square root of 2 divided by 2 cm

• 4.5 cm

What equation would you set up to find the leg length if the hypotenuse is given as 9 cm?

• X divided by 2 = 9

• X square root of 2 = 9

• X = 9

• X square root of 3 = 9

What is the simplified form of X when the hypotenuse is 9 cm?

• 9 divided by square root of 2

• 9 divided by 2

• 9 square root of 2

• 9 square root of 2 divided by 2

What is the key to solving any 45-45-90 triangle?

• Knowing the area

• Knowing the perimeter

• Matching the given information with the reference triangle

• Knowing the angles