45-45-90 Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If the length of each leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.

Front

If the hypotenuse of a 45-45-90 triangle is 8, what is the length of each leg?

Back

Each leg is 8/√2 or 4√2.

Front

What is the area of a 45-45-90 triangle with legs of length 5?

Back

Area = (1/2) × leg × leg = (1/2) × 5 × 5 = 12.5.

Front

How do you derive the lengths of the sides in a 45-45-90 triangle?

Back

By using the Pythagorean theorem, where the sum of the squares of the legs equals the square of the hypotenuse.

Front

What is the value of x in a 45-45-90 triangle if one leg is 4?

Back

x = 4.

Front

If one leg of a 45-45-90 triangle is 10, what are the lengths of the other leg and the hypotenuse?

Back

Other leg = 10; Hypotenuse = 10√2.

Front

What is the perimeter of a 45-45-90 triangle with legs of length 6?

Back

Perimeter = leg + leg + hypotenuse = 6 + 6 + 6√2.