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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.7

Front

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

Back

Hypotenuse = leg × √2.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.6.G.A.1

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.

Tags

CCSS.8.G.B.8

Front

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

Back

x = 4.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8