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 legs of a 45-45-90 triangle are each 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√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 value of x in a 45-45-90 triangle if one leg is 4?

Back

x = 4√2.

Front

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

Back

By using the properties of isosceles right triangles and the Pythagorean theorem.

Front

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

Back

Area = (1/2) × leg × leg = (1/2) × 6 × 6 = 18.

Front

If one leg of a 45-45-90 triangle is 10, what is the length of the other leg?

Back

The other leg is also 10.

Front

What is the perimeter of a 45-45-90 triangle with legs of length 3?

Back

Perimeter = leg + leg + hypotenuse = 3 + 3 + 3√2.